Sequence Database

A database with 1693109 machine generated integer and decimal sequences.

Displaying result 0-99 of total 409977. [0] [1] [2] [3] [4] ... [4099]

Sequence hr1xwu5kzwtrb

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, more...

integer, strictly-monotonic, +, A000290

a(n)=n²
n≥0
2 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=C(n, sqrt(a(n-1)))²
a(0)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=∑[2*n]-n
∑(a)=partial sums of a
n≥0
6 operations
Arithmetic
a(n)=∑[or(1, 1+a(n-1))]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence z3estk1pvl5oj

0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, 0.005302147353502685, more...

decimal, constant, monotonic, +

a(n)=Stieltjes²
Stieltjes=0.0728... (Stieltjes gamma(1))
n≥0
2 operations
Power

Sequence ytsrrubxukk1

0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, 0.055559737616361585, more...

decimal, constant, monotonic, +

a(n)=CopelandErdős²
CopelandErdős=0.2357... (Copeland-Erdős)
n≥0
2 operations
Power

Sequence ftiy4wjzca3fo

0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, 0.06838079232708538, more...

decimal, constant, monotonic, +

a(n)=Mertens²
Mertens=0.2614... (Mertens)
n≥0
2 operations
Power

Sequence k0vg2yaggkv1h

0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, 0.1159656728177258, more...

decimal, constant, monotonic, +

a(n)=Pólya_D3²
Pólya_D3=0.3405... (Pólya random walk 3D)
n≥0
2 operations
Power

Sequence gdknopf3dwdfm

0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, 0.13984295053959955, more...

decimal, constant, monotonic, +

a(n)=Artins²
Artins=0.3739... (Artins)
n≥0
2 operations
Power

Sequence cvzukdelh2uml

0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, 0.32165151185683644, more...

decimal, constant, monotonic, +

a(n)=W1²
W1=0.5671... (Lambert W)
n≥0
2 operations
Power

Sequence fy4qkt2xudykp

0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, 0.33317792380771866, more...

decimal, constant, monotonic, +

a(n)=γ²
γ=0.5772... (Euler Gamma)
n≥0
2 operations
Power

Sequence gt5znmyhl1itl

0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, 0.4358136231022362, more...

decimal, constant, monotonic, +

a(n)=TwinPrime²
TwinPrime=0.6601... (Twin Prime)
n≥0
2 operations
Power

Sequence 33rpgcbm24vyb

0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, 0.8389929697164259, more...

decimal, constant, monotonic, +

a(n)=G²
G=0.9159... (Catalans)
n≥0
2 operations
Power

Sequence dtkvojyz5vkjg

1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, 1.644619341453265, more...

decimal, constant, monotonic, +

a(n)=GlaisherKinkelin²
GlaisherKinkelin=1.2824... (Glaisher-Kinkelin)
n≥0
2 operations
Power

Sequence c5u2xrg2xenof

1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, 1.77577552159833, more...

decimal, constant, monotonic, +

a(n)=B3²
B3=1.3325... (Mertens B3)
n≥0
2 operations
Power

Sequence z1qmfjwijp0ih

2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, 2.1201542558900823, more...

decimal, constant, monotonic, +

a(n)=Backhouse²
Backhouse=1.456... (Backhouse)
n≥0
2 operations
Power

Sequence ahmjwhffsqldi

2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, 2.618033988749895, more...

decimal, constant, monotonic, +

a(n)=ϕ²
ϕ=1.618... (Golden Ratio)
n≥0
2 operations
Power

Sequence jjtz4dojfl1fb

2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, 2.761206841957498, more...

decimal, constant, monotonic, +

a(n)=QR²
QR=1.6616... (Quadratic Recurrence)
n≥0
2 operations
Power

Sequence 5kda0x5rmarrc

3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, 3.3829757679062378, more...

decimal, constant, monotonic, +

a(n)=Tribonacci²
Tribonacci=1.8392... (Tribonacci)
n≥0
2 operations
Power

Sequence cu1jqkq2uxq0e

7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, 7.211652450025658, more...

decimal, constant, monotonic, +

a(n)=Khintchine²
Khintchine=2.6854... (Khintchine)
n≥0
2 operations
Power

Sequence vuvrmqoabyohk

7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, 7.3890560989306495, more...

decimal, constant, monotonic, +

a(n)=e²
e=2.7182... (Euler e)
n≥0
2 operations
Power

Sequence zgivhzgbv01qd

9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, 9.869604401089358, more...

decimal, constant, monotonic, +

a(n)=π²
π=3.1415... (Pi)
n≥0
2 operations
Power

Sequence 3vtyk43kllych

0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, 0.010000000000000002, more...

decimal, constant, monotonic, +

a(n)=(1/10)²
n≥0
4 operations
Power

Sequence qwy3z1mzvglpp

0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, 0.09, more...

decimal, constant, monotonic, +

a(n)=(3/10)²
n≥0
4 operations
Power

Sequence qomzdpe2wdrae

0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, 0.48999999999999994, more...

decimal, constant, monotonic, +

a(n)=(7/10)²
n≥0
4 operations
Power

Sequence xa3v2qyws53ce

0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81, more...

decimal, constant, monotonic, +

a(n)=(9/10)²
n≥0
4 operations
Power

Sequence 3kkskxt4ou4vg

1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, 1.234567901234568, more...

decimal, constant, monotonic, +

a(n)=(10/9)²
n≥0
4 operations
Power

Sequence cbuozmtzcu2ec

2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, 2.0408163265306123, more...

decimal, constant, monotonic, +

a(n)=(10/7)²
n≥0
4 operations
Power

Sequence htckmxeer5chg

11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, 11.111111111111112, more...

decimal, constant, monotonic, +

a(n)=(10/3)²
n≥0
4 operations
Power

Sequence llkyrrajh4rze

0, -1, -4, -9, -16, -25, -36, -49, -64, -81, -100, -121, -144, -169, -196, -225, -256, -289, -324, -361, -400, -441, -484, -529, -576, -625, -676, -729, -784, -841, -900, -961, -1024, -1089, -1156, -1225, -1296, -1369, -1444, -1521, -1600, -1681, -1764, -1849, -1936, -2025, -2116, -2209, -2304, -2401, more...

integer, strictly-monotonic, -

a(n)=-n²
n≥0
3 operations
Power
a(n)=n*floor(-n)
n≥0
5 operations
Arithmetic
a(n)=a(n-1)-Δ[n²]
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=∑[or(1, a(n-1)-2)]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=n-lcm(1+n, n)
lcm(a,b)=least common multiple
n≥0
7 operations
Divisibility

Sequence hksx4gpk5yhnp

-10, -9, -6, -1, 6, 15, 26, 39, 54, 71, 90, 111, 134, 159, 186, 215, 246, 279, 314, 351, 390, 431, 474, 519, 566, 615, 666, 719, 774, 831, 890, 951, 1014, 1079, 1146, 1215, 1286, 1359, 1434, 1511, 1590, 1671, 1754, 1839, 1926, 2015, 2106, 2199, 2294, 2391, more...

integer, strictly-monotonic, +-

a(n)=n²-10
n≥0
4 operations
Power

Sequence hhbbgkkmn4mkd

-9, -8, -5, 0, 7, 16, 27, 40, 55, 72, 91, 112, 135, 160, 187, 216, 247, 280, 315, 352, 391, 432, 475, 520, 567, 616, 667, 720, 775, 832, 891, 952, 1015, 1080, 1147, 1216, 1287, 1360, 1435, 1512, 1591, 1672, 1755, 1840, 1927, 2016, 2107, 2200, 2295, 2392, more...

integer, strictly-monotonic, +-

a(n)=n²-9
n≥0
4 operations
Power
a(n)=(3+n)*(n-3)
n≥0
7 operations
Arithmetic

Sequence n2fguxjoiii0h

-8, -7, -4, 1, 8, 17, 28, 41, 56, 73, 92, 113, 136, 161, 188, 217, 248, 281, 316, 353, 392, 433, 476, 521, 568, 617, 668, 721, 776, 833, 892, 953, 1016, 1081, 1148, 1217, 1288, 1361, 1436, 1513, 1592, 1673, 1756, 1841, 1928, 2017, 2108, 2201, 2296, 2393, more...

integer, strictly-monotonic, +-

a(n)=n²-8
n≥0
4 operations
Power

Sequence zapbulfn0r2ub

-7, -6, -3, 2, 9, 18, 29, 42, 57, 74, 93, 114, 137, 162, 189, 218, 249, 282, 317, 354, 393, 434, 477, 522, 569, 618, 669, 722, 777, 834, 893, 954, 1017, 1082, 1149, 1218, 1289, 1362, 1437, 1514, 1593, 1674, 1757, 1842, 1929, 2018, 2109, 2202, 2297, 2394, more...

integer, strictly-monotonic, +-

a(n)=n²-7
n≥0
4 operations
Power

Sequence u1oeau5d3bg0d

-6, -5, -2, 3, 10, 19, 30, 43, 58, 75, 94, 115, 138, 163, 190, 219, 250, 283, 318, 355, 394, 435, 478, 523, 570, 619, 670, 723, 778, 835, 894, 955, 1018, 1083, 1150, 1219, 1290, 1363, 1438, 1515, 1594, 1675, 1758, 1843, 1930, 2019, 2110, 2203, 2298, 2395, more...

integer, strictly-monotonic, +-

a(n)=n²-6
n≥0
4 operations
Power

Sequence z21rgumvzncej

-5, -4, -1, 4, 11, 20, 31, 44, 59, 76, 95, 116, 139, 164, 191, 220, 251, 284, 319, 356, 395, 436, 479, 524, 571, 620, 671, 724, 779, 836, 895, 956, 1019, 1084, 1151, 1220, 1291, 1364, 1439, 1516, 1595, 1676, 1759, 1844, 1931, 2020, 2111, 2204, 2299, 2396, more...

integer, strictly-monotonic, +-, A028875

a(n)=n²-5
n≥0
4 operations
Power

Sequence umdnc3z43hihf

-4, -3, 0, 5, 12, 21, 32, 45, 60, 77, 96, 117, 140, 165, 192, 221, 252, 285, 320, 357, 396, 437, 480, 525, 572, 621, 672, 725, 780, 837, 896, 957, 1020, 1085, 1152, 1221, 1292, 1365, 1440, 1517, 1596, 1677, 1760, 1845, 1932, 2021, 2112, 2205, 2300, 2397, more...

integer, strictly-monotonic, +-

a(n)=n²-4
n≥0
4 operations
Power
a(n)=(2+n)*(n-2)
n≥0
7 operations
Arithmetic

Sequence ziscigisk4f0g

-3, -2, 1, 6, 13, 22, 33, 46, 61, 78, 97, 118, 141, 166, 193, 222, 253, 286, 321, 358, 397, 438, 481, 526, 573, 622, 673, 726, 781, 838, 897, 958, 1021, 1086, 1153, 1222, 1293, 1366, 1441, 1518, 1597, 1678, 1761, 1846, 1933, 2022, 2113, 2206, 2301, 2398, more...

integer, strictly-monotonic, +-

a(n)=n²-3
n≥0
4 operations
Power

Sequence gt2uucal13cle

-2, -1, 2, 7, 14, 23, 34, 47, 62, 79, 98, 119, 142, 167, 194, 223, 254, 287, 322, 359, 398, 439, 482, 527, 574, 623, 674, 727, 782, 839, 898, 959, 1022, 1087, 1154, 1223, 1294, 1367, 1442, 1519, 1598, 1679, 1762, 1847, 1934, 2023, 2114, 2207, 2302, 2399, more...

integer, strictly-monotonic, +-

a(n)=n²-2
n≥0
4 operations
Power
a(n)=n-∑[a(n-1)-2]
a(0)=2
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence 31gukq4exqhcd

-1, 0, 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, 624, 675, 728, 783, 840, 899, 960, 1023, 1088, 1155, 1224, 1295, 1368, 1443, 1520, 1599, 1680, 1763, 1848, 1935, 2024, 2115, 2208, 2303, 2400, more...

integer, strictly-monotonic, +-

a(n)=n²-1
n≥0
4 operations
Power
a(n)=-∑[a(n-1)-2]
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[2*n-1]
∑(a)=partial sums of a
n≥0
6 operations
Arithmetic
a(n)=n²-pt(∑[n])
∑(a)=partial sums of a
pt(n)=Pascals triangle by rows
n≥0
6 operations
Combinatoric
a(n)=n²-C(n, n²)
C(n,k)=binomial coefficient
n≥0
7 operations
Combinatoric

Sequence izjk4qlv2l1io

0, 0.010000000000000002, 0.04000000000000001, 0.09, 0.16000000000000003, 0.25, 0.36, 0.48999999999999994, 0.6400000000000001, 0.81, 1, 1.2100000000000002, 1.44, 1.6900000000000002, 1.9599999999999997, 2.25, 2.5600000000000005, 2.8899999999999997, 3.24, 3.61, 4, 4.41, 4.840000000000001, 5.289999999999999, 5.76, more...

decimal, strictly-monotonic, +

a(n)=(n/10)²
n≥0
4 operations
Power

Sequence 3qcwiev4q4gnh

0, 0.012345679012345678, 0.04938271604938271, 0.1111111111111111, 0.19753086419753085, 0.308641975308642, 0.4444444444444444, 0.6049382716049383, 0.7901234567901234, 1, 1.234567901234568, 1.4938271604938274, 1.7777777777777777, 2.0864197530864197, 2.419753086419753, 2.777777777777778, 3.1604938271604937, 3.567901234567901, 4, 4.45679012345679, 4.938271604938272, 5.4444444444444455, 5.975308641975309, 6.530864197530863, 7.111111111111111, more...

decimal, strictly-monotonic, +

a(n)=(n/9)²
n≥0
4 operations
Power

Sequence ie5me2p5uf4ee

0, 0.015625, 0.0625, 0.140625, 0.25, 0.390625, 0.5625, 0.765625, 1, 1.265625, 1.5625, 1.890625, 2.25, 2.640625, 3.0625, 3.515625, 4, 4.515625, 5.0625, 5.640625, 6.25, 6.890625, 7.5625, 8.265625, 9, more...

decimal, strictly-monotonic, +

a(n)=(n/8)²
n≥0
4 operations
Power

Sequence lj0ja51zxpqnj

0, 0.02040816326530612, 0.08163265306122448, 0.18367346938775508, 0.32653061224489793, 0.5102040816326531, 0.7346938775510203, 1, 1.3061224489795917, 1.6530612244897962, 2.0408163265306123, 2.4693877551020407, 2.9387755102040813, 3.4489795918367347, 4, 4.591836734693877, 5.224489795918367, 5.897959183673469, 6.612244897959185, 7.367346938775511, 8.16326530612245, 9, 9.877551020408163, 10.795918367346937, 11.755102040816325, more...

decimal, strictly-monotonic, +

a(n)=(n/7)²
n≥0
4 operations
Power

Sequence x1swia0eh5ngd

0, 0.027777777777777776, 0.1111111111111111, 0.25, 0.4444444444444444, 0.6944444444444445, 1, 1.3611111111111114, 1.7777777777777777, 2.25, 2.777777777777778, 3.3611111111111107, 4, 4.694444444444444, 5.4444444444444455, 6.25, 7.111111111111111, 8.027777777777779, 9, 10.027777777777777, 11.111111111111112, 12.25, 13.444444444444443, 14.694444444444446, 16, more...

decimal, strictly-monotonic, +

a(n)=(n/6)²
n≥0
4 operations
Power

Sequence k4oom20lfqvwc

0, 0.04000000000000001, 0.16000000000000003, 0.36, 0.6400000000000001, 1, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4, 4.840000000000001, 5.76, 6.760000000000001, 7.839999999999999, 9, 10.240000000000002, 11.559999999999999, 12.96, 14.44, 16, 17.64, 19.360000000000003, 21.159999999999997, 23.04, more...

decimal, strictly-monotonic, +

a(n)=(n/5)²
n≥0
4 operations
Power

Sequence dmwaxguzde1ko

0, 0.0625, 0.25, 0.5625, 1, 1.5625, 2.25, 3.0625, 4, 5.0625, 6.25, 7.5625, 9, 10.5625, 12.25, 14.0625, 16, 18.0625, 20.25, 22.5625, 25, 27.5625, 30.25, 33.0625, 36, more...

decimal, strictly-monotonic, +

a(n)=(n/4)²
n≥0
4 operations
Power

Sequence 3gs5bc43k4etj

0, 0.1, 0.4, 0.9, 1.6, 2.5, 3.6, 4.9, 6.4, 8.1, 10, 12.1, 14.4, 16.9, 19.6, 22.5, 25.6, 28.9, 32.4, 36.1, 40, 44.1, 48.4, 52.9, 57.6, more...

decimal, strictly-monotonic, +

a(n)=n²/10
n≥0
4 operations
Power

Sequence 2zhc2uhmcnefk

0, 0.1111111111111111, 0.4444444444444444, 1, 1.7777777777777777, 2.7777777777777777, 4, 5.444444444444445, 7.111111111111111, 9, 11.11111111111111, 13.444444444444445, 16, 18.77777777777778, 21.77777777777778, 25, 28.444444444444443, 32.111111111111114, 36, 40.111111111111114, 44.44444444444444, 49, 53.77777777777778, 58.77777777777778, 64, more...

decimal, strictly-monotonic, +

a(n)=n²/9
n≥0
4 operations
Power

Sequence cygg0b2ob2fle

0, 0.1111111111111111, 0.4444444444444444, 1, 1.7777777777777777, 2.777777777777778, 4, 5.4444444444444455, 7.111111111111111, 9, 11.111111111111112, 13.444444444444443, 16, 18.777777777777775, 21.777777777777782, 25, 28.444444444444443, 32.111111111111114, 36, 40.11111111111111, 44.44444444444445, 49, 53.77777777777777, 58.777777777777786, 64, more...

decimal, strictly-monotonic, +

a(n)=(n/3)²
n≥0
4 operations
Power

Sequence mdyyynh4z52wj

0, 0.125, 0.5, 1.125, 2, 3.125, 4.5, 6.125, 8, 10.125, 12.5, 15.125, 18, 21.125, 24.5, 28.125, 32, 36.125, 40.5, 45.125, 50, 55.125, 60.5, 66.125, 72, more...

decimal, strictly-monotonic, +

a(n)=n²/8
n≥0
4 operations
Power
a(n)=n*n/8
n≥0
5 operations
Arithmetic

Sequence ctm510litewuo

0, 0.14285714285714285, 0.5714285714285714, 1.2857142857142858, 2.2857142857142856, 3.5714285714285716, 5.142857142857143, 7, 9.142857142857142, 11.571428571428571, 14.285714285714286, 17.285714285714285, 20.571428571428573, 24.142857142857142, 28, 32.142857142857146, 36.57142857142857, 41.285714285714285, 46.285714285714285, 51.57142857142857, 57.142857142857146, 63, 69.14285714285714, 75.57142857142857, 82.28571428571429, more...

decimal, strictly-monotonic, +

a(n)=n²/7
n≥0
4 operations
Power

Sequence dstfbtcj3zpx

0, 0.16666666666666666, 0.6666666666666666, 1.5, 2.6666666666666665, 4.166666666666667, 6, 8.166666666666666, 10.666666666666666, 13.5, 16.666666666666668, 20.166666666666668, 24, 28.166666666666668, 32.666666666666664, 37.5, 42.666666666666664, 48.166666666666664, 54, 60.166666666666664, 66.66666666666667, 73.5, 80.66666666666667, 88.16666666666667, 96, more...

decimal, strictly-monotonic, +

a(n)=n²/6
n≥0
4 operations
Power
a(n)=n*n/2/3
n≥0
7 operations
Arithmetic

Sequence palrtwfwcxoqc

0, 0.2, 0.8, 1.8, 3.2, 5, 7.2, 9.8, 12.8, 16.2, 20, 24.2, 28.8, 33.8, 39.2, 45, 51.2, 57.8, 64.8, 72.2, 80, 88.2, 96.8, 105.8, 115.2, more...

decimal, strictly-monotonic, +

a(n)=n²/5
n≥0
4 operations
Power

Sequence zo4mmluddtpdd

0, 0.25, 1, 2.25, 4, 6.25, 9, 12.25, 16, 20.25, 25, 30.25, 36, 42.25, 49, 56.25, 64, 72.25, 81, 90.25, 100, 110.25, 121, 132.25, 144, more...

decimal, strictly-monotonic, +

a(n)=(n/2)²
n≥0
4 operations
Power
a(n)=n*n/4
n≥0
5 operations
Arithmetic

Sequence nmt423pskfxjb

0, 0.5, 2, 4.5, 8, 12.5, 18, 24.5, 32, 40.5, 50, 60.5, 72, 84.5, 98, 112.5, 128, 144.5, 162, 180.5, 200, 220.5, 242, 264.5, 288, more...

decimal, strictly-monotonic, +

a(n)=n²/2
n≥0
4 operations
Power
a(n)=n*n/2
n≥0
5 operations
Arithmetic
a(n)=n-1/2+a(n-1)
a(0)=0
n≥0
7 operations
Recursive

Sequence try5v0k0dtwbj

0, 2, 8, 18, 32, 50, 72, 98, 128, 162, 200, 242, 288, 338, 392, 450, 512, 578, 648, 722, 800, 882, 968, 1058, 1152, 1250, 1352, 1458, 1568, 1682, 1800, 1922, 2048, 2178, 2312, 2450, 2592, 2738, 2888, 3042, 3200, 3362, 3528, 3698, 3872, 4050, 4232, 4418, 4608, 4802, more...

integer, strictly-monotonic, +, A001105

a(n)=2*n²
n≥0
4 operations
Power
a(n)=n*2*n
n≥0
5 operations
Arithmetic
a(n)=∑[or(2, 2+a(n-1))]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=gcd(a(n-1), 2)*n²
a(0)=0
gcd(a,b)=greatest common divisor
n≥0
6 operations
Recursive
a(n)=n*lcm(2*n, 2)
lcm(a,b)=least common multiple
n≥0
7 operations
Divisibility

Sequence hidua355lzald

0, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 363, 432, 507, 588, 675, 768, 867, 972, 1083, 1200, 1323, 1452, 1587, 1728, 1875, 2028, 2187, 2352, 2523, 2700, 2883, 3072, 3267, 3468, 3675, 3888, 4107, 4332, 4563, 4800, 5043, 5292, 5547, 5808, 6075, 6348, 6627, 6912, 7203, more...

integer, strictly-monotonic, +, A033428

a(n)=3*n²
n≥0
4 operations
Power
a(n)=n*3*n
n≥0
5 operations
Arithmetic
a(n)=gcd(a(n-1), 3)*n²
a(0)=0
gcd(a,b)=greatest common divisor
n≥0
6 operations
Recursive
a(n)=n*∑[or(a(n-1), a(n-2))]
a(0)=1
a(1)=2
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=n*lcm(3*n, 3)
lcm(a,b)=least common multiple
n≥0
7 operations
Divisibility

Sequence 0yffdynyo3vkp

0, 4, 16, 36, 64, 100, 144, 196, 256, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744, 8100, 8464, 8836, 9216, 9604, more...

integer, strictly-monotonic, +, A016742

a(n)=(2*n)²
n≥0
4 operations
Power
a(n)=n*4*n
n≥0
5 operations
Arithmetic
a(n)=(2+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence cgoyje0efstnb

0, 5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 605, 720, 845, 980, 1125, 1280, 1445, 1620, 1805, 2000, 2205, 2420, 2645, 2880, 3125, 3380, 3645, 3920, 4205, 4500, 4805, 5120, 5445, 5780, 6125, 6480, 6845, 7220, 7605, 8000, 8405, 8820, 9245, 9680, 10125, 10580, 11045, 11520, 12005, more...

integer, strictly-monotonic, +, A033429

a(n)=5*n²
n≥0
4 operations
Power
a(n)=n*5*n
n≥0
5 operations
Arithmetic

Sequence dkkwshlkrqtdj

0, 6, 24, 54, 96, 150, 216, 294, 384, 486, 600, 726, 864, 1014, 1176, 1350, 1536, 1734, 1944, 2166, 2400, 2646, 2904, 3174, 3456, 3750, 4056, 4374, 4704, 5046, 5400, 5766, 6144, 6534, 6936, 7350, 7776, 8214, 8664, 9126, 9600, 10086, 10584, 11094, 11616, 12150, 12696, 13254, 13824, 14406, more...

integer, strictly-monotonic, +, A033581

a(n)=6*n²
n≥0
4 operations
Power
a(n)=n*6*n
n≥0
5 operations
Arithmetic

Sequence nogpzr4wk54ll

0, 7, 28, 63, 112, 175, 252, 343, 448, 567, 700, 847, 1008, 1183, 1372, 1575, 1792, 2023, 2268, 2527, 2800, 3087, 3388, 3703, 4032, 4375, 4732, 5103, 5488, 5887, 6300, 6727, 7168, 7623, 8092, 8575, 9072, 9583, 10108, 10647, 11200, 11767, 12348, 12943, 13552, 14175, 14812, 15463, 16128, 16807, more...

integer, strictly-monotonic, +, A033582

a(n)=7*n²
n≥0
4 operations
Power
a(n)=n*7*n
n≥0
5 operations
Arithmetic

Sequence lakhyrv3ku1sk

0, 8, 32, 72, 128, 200, 288, 392, 512, 648, 800, 968, 1152, 1352, 1568, 1800, 2048, 2312, 2592, 2888, 3200, 3528, 3872, 4232, 4608, 5000, 5408, 5832, 6272, 6728, 7200, 7688, 8192, 8712, 9248, 9800, 10368, 10952, 11552, 12168, 12800, 13448, 14112, 14792, 15488, 16200, 16928, 17672, 18432, 19208, more...

integer, strictly-monotonic, +, A139098

a(n)=8*n²
n≥0
4 operations
Power
a(n)=n*8*n
n≥0
5 operations
Arithmetic

Sequence iuo24bpbvshdg

0, 9, 36, 81, 144, 225, 324, 441, 576, 729, 900, 1089, 1296, 1521, 1764, 2025, 2304, 2601, 2916, 3249, 3600, 3969, 4356, 4761, 5184, 5625, 6084, 6561, 7056, 7569, 8100, 8649, 9216, 9801, 10404, 11025, 11664, 12321, 12996, 13689, 14400, 15129, 15876, 16641, 17424, 18225, 19044, 19881, 20736, 21609, more...

integer, strictly-monotonic, +, A016766

a(n)=(3*n)²
n≥0
4 operations
Power
a(n)=n*9*n
n≥0
5 operations
Arithmetic
a(n)=(3+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive
a(n)=n*∑[τ(a(n-1))²]
a(0)=5
τ(n)=number of divisors of n
∑(a)=partial sums of a
n≥0
6 operations
Prime

Sequence nt20sbikc2vun

0, 10, 40, 90, 160, 250, 360, 490, 640, 810, 1000, 1210, 1440, 1690, 1960, 2250, 2560, 2890, 3240, 3610, 4000, 4410, 4840, 5290, 5760, 6250, 6760, 7290, 7840, 8410, 9000, 9610, 10240, 10890, 11560, 12250, 12960, 13690, 14440, 15210, 16000, 16810, 17640, 18490, 19360, 20250, 21160, 22090, 23040, 24010, more...

integer, strictly-monotonic, +, A033583

a(n)=10*n²
n≥0
4 operations
Power
a(n)=n*10*n
n≥0
5 operations
Arithmetic

Sequence cg22u22pynovf

0, 16, 64, 144, 256, 400, 576, 784, 1024, 1296, 1600, 1936, 2304, 2704, 3136, 3600, 4096, 4624, 5184, 5776, 6400, 7056, 7744, 8464, 9216, 10000, 10816, 11664, 12544, 13456, 14400, 15376, 16384, 17424, 18496, 19600, 20736, 21904, 23104, 24336, 25600, 26896, 28224, 29584, 30976, 32400, 33856, 35344, 36864, 38416, more...

integer, strictly-monotonic, +, A016802

a(n)=(4*n)²
n≥0
4 operations
Power
a(n)=(4+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence zh4wrywdgztaj

0, 25, 100, 225, 400, 625, 900, 1225, 1600, 2025, 2500, 3025, 3600, 4225, 4900, 5625, 6400, 7225, 8100, 9025, 10000, 11025, 12100, 13225, 14400, 15625, 16900, 18225, 19600, 21025, 22500, 24025, 25600, 27225, 28900, 30625, 32400, 34225, 36100, 38025, 40000, 42025, 44100, 46225, 48400, 50625, 52900, 55225, 57600, 60025, more...

integer, strictly-monotonic, +, A016850

a(n)=(5*n)²
n≥0
4 operations
Power
a(n)=(5+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence 2aomdg1wndgjo

0, 36, 144, 324, 576, 900, 1296, 1764, 2304, 2916, 3600, 4356, 5184, 6084, 7056, 8100, 9216, 10404, 11664, 12996, 14400, 15876, 17424, 19044, 20736, 22500, 24336, 26244, 28224, 30276, 32400, 34596, 36864, 39204, 41616, 44100, 46656, 49284, 51984, 54756, 57600, 60516, 63504, 66564, 69696, 72900, 76176, 79524, 82944, 86436, more...

integer, strictly-monotonic, +, A016910

a(n)=(6*n)²
n≥0
4 operations
Power
a(n)=(6+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence kfcagrrdd3dnn

0, 49, 196, 441, 784, 1225, 1764, 2401, 3136, 3969, 4900, 5929, 7056, 8281, 9604, 11025, 12544, 14161, 15876, 17689, 19600, 21609, 23716, 25921, 28224, 30625, 33124, 35721, 38416, 41209, 44100, 47089, 50176, 53361, 56644, 60025, 63504, 67081, 70756, 74529, 78400, 82369, 86436, 90601, 94864, 99225, 103684, 108241, 112896, 117649, more...

integer, strictly-monotonic, +, A016982

a(n)=(7*n)²
n≥0
4 operations
Power
a(n)=(7+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence 5cradg5s5punf

0, 64, 256, 576, 1024, 1600, 2304, 3136, 4096, 5184, 6400, 7744, 9216, 10816, 12544, 14400, 16384, 18496, 20736, 23104, 25600, 28224, 30976, 33856, 36864, 40000, 43264, 46656, 50176, 53824, 57600, 61504, 65536, 69696, 73984, 78400, 82944, 87616, 92416, 97344, 102400, 107584, 112896, 118336, 123904, 129600, 135424, 141376, 147456, 153664, more...

integer, strictly-monotonic, +, A017066

a(n)=(8*n)²
n≥0
4 operations
Power
a(n)=(8+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence qbf3vva40obdg

0, 81, 324, 729, 1296, 2025, 2916, 3969, 5184, 6561, 8100, 9801, 11664, 13689, 15876, 18225, 20736, 23409, 26244, 29241, 32400, 35721, 39204, 42849, 46656, 50625, 54756, 59049, 63504, 68121, 72900, 77841, 82944, 88209, 93636, 99225, 104976, 110889, 116964, 123201, 129600, 136161, 142884, 149769, 156816, 164025, 171396, 178929, 186624, 194481, more...

integer, strictly-monotonic, +, A017162

a(n)=(9*n)²
n≥0
4 operations
Power
a(n)=(9+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence pc1nuae11l4jn

0, 100, 400, 900, 1600, 2500, 3600, 4900, 6400, 8100, 10000, 12100, 14400, 16900, 19600, 22500, 25600, 28900, 32400, 36100, 40000, 44100, 48400, 52900, 57600, 62500, 67600, 72900, 78400, 84100, 90000, 96100, 102400, 108900, 115600, 122500, 129600, 136900, 144400, 152100, 160000, 168100, 176400, 184900, 193600, 202500, 211600, 220900, 230400, 240100, more...

integer, strictly-monotonic, +, A017270

a(n)=(10*n)²
n≥0
4 operations
Power
a(n)=(10+sqrt(a(n-1)))²
a(0)=0
n≥0
5 operations
Recursive

Sequence erjiokpuibizk

1, 0, -3, -8, -15, -24, -35, -48, -63, -80, -99, -120, -143, -168, -195, -224, -255, -288, -323, -360, -399, -440, -483, -528, -575, -624, -675, -728, -783, -840, -899, -960, -1023, -1088, -1155, -1224, -1295, -1368, -1443, -1520, -1599, -1680, -1763, -1848, -1935, -2024, -2115, -2208, -2303, -2400, more...

integer, strictly-monotonic, +-, A258837

a(n)=1-n²
n≥0
4 operations
Power
a(n)=∑[a(n-1)-2]
a(0)=1
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑[1-2*n]
∑(a)=partial sums of a
n≥0
6 operations
Arithmetic
a(n)=∑[xor(1, a(n-1)-3)]
a(0)=1
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=∑[or(1, a(n-1)-2)]
a(0)=1
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence jdt1yupfh4wgp

1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, more...

integer, non-monotonic, +, A174902

a(n)=(1-n)²
n≥0
4 operations
Power
a(n)=(n-pt(∑[n]))²
∑(a)=partial sums of a
pt(n)=Pascals triangle by rows
n≥0
6 operations
Combinatoric
a(n)=(n-agc(agc(a(n-1))))²
a(0)=1
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
6 operations
Prime
a(n)=1-n*(2-n)
n≥0
7 operations
Arithmetic
a(n)=((2-n)*λ(n))²
λ(n)=Liouville's function
n≥1
7 operations
Prime

Sequence txyxvdyhhti0o

1, 0.25, 0.1111111111111111, 0.0625, 0.04000000000000001, 0.027777777777777776, 0.02040816326530612, 0.015625, 0.012345679012345678, 0.010000000000000002, 0.008264462809917356, 0.006944444444444444, 0.00591715976331361, 0.00510204081632653, 0.004444444444444444, 0.00390625, 0.003460207612456748, 0.00308641975308642, 0.002770083102493074, 0.0025, 0.002267573696145124, 0.002066115702479339, 0.001890359168241966, 0.001736111111111111, 0.0016, more...

decimal, strictly-monotonic, convergent, +

a(n)=(1/n)²
n≥1
4 operations
Power
a(n)=(λ(n)/n)²
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=(C(n, n²)/n)²
C(n,k)=binomial coefficient
n≥1
7 operations
Combinatoric
a(n)=(φ(n)/φ(n²))²
ϕ(n)=number of relative primes (Euler's totient)
n≥1
7 operations
Prime
a(n)=(agc(agc(n)²)/n)²
agc(n)=number of factorizations into prime powers (abelian group count)
n≥1
7 operations
Prime

Sequence t4hdbuk4oppgh

1, 0.25, 0.1111111111111111, 0.0625, 0.04, 0.027777777777777776, 0.02040816326530612, 0.015625, 0.012345679012345678, 0.01, 0.008264462809917356, 0.006944444444444444, 0.005917159763313609, 0.00510204081632653, 0.004444444444444444, 0.00390625, 0.003460207612456748, 0.00308641975308642, 0.002770083102493075, 0.0025, 0.002267573696145125, 0.002066115702479339, 0.001890359168241966, 0.001736111111111111, 0.0016, more...

decimal, strictly-monotonic, convergent, +

a(n)=1/n²
n≥1
4 operations
Power
a(n)=1/∑[2+a(n-1)]
a(0)=1
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=λ(n²)/n²
λ(n)=Liouville's function
n≥1
6 operations
Prime
a(n)=1/(n/(1/n))
n≥1
7 operations
Arithmetic
a(n)=C(n, n²)/n²
C(n,k)=binomial coefficient
n≥1
7 operations
Combinatoric

Sequence cxa0mydrpuitj

1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 325, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1297, 1370, 1445, 1522, 1601, 1682, 1765, 1850, 1937, 2026, 2117, 2210, 2305, 2402, more...

integer, strictly-monotonic, +, A002522

a(n)=1+n²
n≥0
4 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=1
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=n²+pt(∑[n])
∑(a)=partial sums of a
pt(n)=Pascals triangle by rows
n≥0
6 operations
Combinatoric
a(n)=n²+C(n, a(n-1))
a(0)=1
C(n,k)=binomial coefficient
n≥0
6 operations
Combinatoric
a(n)=2*(1+a(n-1))-a(n-2)
a(0)=1
a(1)=2
n≥0
7 operations
Recursive

Sequence 5gqj5n4epqqfn

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, more...

integer, strictly-monotonic, +

a(n)=(1+n)²
n≥0
4 operations
Power
a(n)=∑[2+a(n-1)]
a(0)=1
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=n/(1/n)
n≥1
5 operations
Arithmetic
a(n)=(n*λ(n))²
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=lcm(n, gpf(n))²
gpf(n)=greatest prime factor of n
lcm(a,b)=least common multiple
n≥1
5 operations
Prime

Sequence cwq4vocwlgm4g

2, 0.5, 0.2222222222222222, 0.125, 0.08, 0.05555555555555555, 0.04081632653061224, 0.03125, 0.024691358024691357, 0.02, 0.01652892561983471, 0.013888888888888888, 0.011834319526627219, 0.01020408163265306, 0.008888888888888889, 0.0078125, 0.006920415224913495, 0.006172839506172839, 0.00554016620498615, 0.005, 0.00453514739229025, 0.004132231404958678, 0.003780718336483932, 0.003472222222222222, 0.0032, more...

decimal, strictly-monotonic, convergent, +

a(n)=2/n²
n≥1
4 operations
Power
a(n)=2/∑[2+a(n-1)]
a(0)=1
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=1/(n/(2/n))
n≥1
7 operations
Arithmetic
a(n)=2/(n*λ(n))²
λ(n)=Liouville's function
n≥1
7 operations
Prime
a(n)=lpf(2*n)/n²
lpf(n)=least prime factor of n
n≥1
7 operations
Prime

Sequence my40xjvgwplqb

2, 1, -2, -7, -14, -23, -34, -47, -62, -79, -98, -119, -142, -167, -194, -223, -254, -287, -322, -359, -398, -439, -482, -527, -574, -623, -674, -727, -782, -839, -898, -959, -1022, -1087, -1154, -1223, -1294, -1367, -1442, -1519, -1598, -1679, -1762, -1847, -1934, -2023, -2114, -2207, -2302, -2399, more...

integer, strictly-monotonic, +-

a(n)=2-n²
n≥0
4 operations
Power
a(n)=a(n-1)-Δ[n²]
a(0)=2
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=∑[or(1, a(n-1)-3)]
a(0)=2
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence cfrwlrfyvi3qj

2, 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403, more...

integer, strictly-monotonic, +, A059100

a(n)=2+n²
n≥0
4 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=2
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=2+(n%p(a(n-1)))²
a(0)=2
p(n)=nth prime
n≥0
7 operations
Prime
a(n)=n²+lpf(a(n-1)+a(n-1))
a(0)=2
lpf(n)=least prime factor of n
n≥0
7 operations
Prime

Sequence p5oeny4prfnqm

3, 0.75, 0.3333333333333333, 0.1875, 0.12, 0.08333333333333333, 0.061224489795918366, 0.046875, 0.037037037037037035, 0.03, 0.024793388429752067, 0.020833333333333332, 0.01775147928994083, 0.015306122448979591, 0.013333333333333334, 0.01171875, 0.010380622837370242, 0.009259259259259259, 0.008310249307479225, 0.0075, 0.006802721088435374, 0.006198347107438017, 0.005671077504725898, 0.005208333333333333, 0.0048, more...

decimal, strictly-monotonic, convergent, +

a(n)=3/n²
n≥1
4 operations
Power
a(n)=3/∑[2+a(n-1)]
a(0)=1
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=3/(n/(1/n))
n≥1
7 operations
Arithmetic
a(n)=3/(n*λ(n))²
λ(n)=Liouville's function
n≥1
7 operations
Prime
a(n)=τ(p(n)²)/n²
p(n)=nth prime
τ(n)=number of divisors of n
n≥1
7 operations
Prime

Sequence sganhfjkwihap

3, 2, -1, -6, -13, -22, -33, -46, -61, -78, -97, -118, -141, -166, -193, -222, -253, -286, -321, -358, -397, -438, -481, -526, -573, -622, -673, -726, -781, -838, -897, -958, -1021, -1086, -1153, -1222, -1293, -1366, -1441, -1518, -1597, -1678, -1761, -1846, -1933, -2022, -2113, -2206, -2301, -2398, more...

integer, strictly-monotonic, +-

a(n)=3-n²
n≥0
4 operations
Power
a(n)=a(n-1)-Δ[n²]
a(0)=3
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=xor(2, ∑[a(n-1)-2])
a(0)=1
∑(a)=partial sums of a
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Recursive
a(n)=or(2, ∑[a(n-1)-2])
a(0)=1
∑(a)=partial sums of a
or(a,b)=bitwise or
n≥0
6 operations
Recursive

Sequence jnsex5wkdjfxf

3, 4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 124, 147, 172, 199, 228, 259, 292, 327, 364, 403, 444, 487, 532, 579, 628, 679, 732, 787, 844, 903, 964, 1027, 1092, 1159, 1228, 1299, 1372, 1447, 1524, 1603, 1684, 1767, 1852, 1939, 2028, 2119, 2212, 2307, 2404, more...

integer, strictly-monotonic, +, A117950

a(n)=3+n²
n≥0
4 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=3
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence yecf3cin15jjd

4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, more...

integer, non-monotonic, +

a(n)=(2-n)²
n≥0
4 operations
Power
a(n)=((3-n)*λ(n))²
λ(n)=Liouville's function
n≥1
7 operations
Prime
a(n)=(2-n)*floor(2-n)
n≥0
8 operations
Arithmetic

Sequence 3g1rbkkhpp3uo

4, 1, 0.4444444444444444, 0.25, 0.16000000000000003, 0.1111111111111111, 0.08163265306122448, 0.0625, 0.04938271604938271, 0.04000000000000001, 0.03305785123966942, 0.027777777777777776, 0.02366863905325444, 0.02040816326530612, 0.017777777777777778, 0.015625, 0.01384083044982699, 0.012345679012345678, 0.011080332409972297, 0.010000000000000002, 0.009070294784580497, 0.008264462809917356, 0.007561436672967863, 0.006944444444444444, 0.0064, more...

decimal, strictly-monotonic, convergent, +

a(n)=(2/n)²
n≥1
4 operations
Power
a(n)=(2/(n*λ(n)))²
λ(n)=Liouville's function
n≥1
7 operations
Prime
a(n)=(lpf(2*n)/n)²
lpf(n)=least prime factor of n
n≥1
7 operations
Prime
a(n)=(Ω(p(n)²)/n)²
p(n)=nth prime
Ω(n)=max distinct factors of n
n≥1
7 operations
Prime

Sequence gv2ga24hpos0p

4, 3, 0, -5, -12, -21, -32, -45, -60, -77, -96, -117, -140, -165, -192, -221, -252, -285, -320, -357, -396, -437, -480, -525, -572, -621, -672, -725, -780, -837, -896, -957, -1020, -1085, -1152, -1221, -1292, -1365, -1440, -1517, -1596, -1677, -1760, -1845, -1932, -2021, -2112, -2205, -2300, -2397, more...

integer, strictly-monotonic, +-

a(n)=4-n²
n≥0
4 operations
Power
a(n)=a(n-1)-Δ[n²]
a(0)=4
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=(2+n)*(2-n)
n≥0
7 operations
Arithmetic

Sequence fwbo02kfdyphh

4, 5, 8, 13, 20, 29, 40, 53, 68, 85, 104, 125, 148, 173, 200, 229, 260, 293, 328, 365, 404, 445, 488, 533, 580, 629, 680, 733, 788, 845, 904, 965, 1028, 1093, 1160, 1229, 1300, 1373, 1448, 1525, 1604, 1685, 1768, 1853, 1940, 2029, 2120, 2213, 2308, 2405, more...

integer, strictly-monotonic, +, A087475

a(n)=4+n²
n≥0
4 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=4
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence 1kdjjm1l4ezxo

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, more...

integer, strictly-monotonic, +

a(n)=(2+n)²
n≥0
4 operations
Power
a(n)=(1+sqrt(a(n-1)))²
a(0)=4
n≥0
5 operations
Recursive
a(n)=(n+λ(n²))²
λ(n)=Liouville's function
n≥1
6 operations
Prime
a(n)=∑[∑[2/pt(a(n-1))]]
a(0)=4
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
6 operations
Combinatoric
a(n)=∑[∑[2/φ(a(n-1))]]
a(0)=4
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥0
6 operations
Prime

Sequence mgqdjja1zwqeb

5, 1.25, 0.5555555555555556, 0.3125, 0.2, 0.1388888888888889, 0.10204081632653061, 0.078125, 0.06172839506172839, 0.05, 0.04132231404958678, 0.034722222222222224, 0.029585798816568046, 0.025510204081632654, 0.022222222222222223, 0.01953125, 0.01730103806228374, 0.015432098765432098, 0.013850415512465374, 0.0125, 0.011337868480725623, 0.010330578512396695, 0.00945179584120983, 0.008680555555555556, 0.008, more...

decimal, strictly-monotonic, convergent, +

a(n)=5/n²
n≥1
4 operations
Power

Sequence e3upj2b14yzz

5, 4, 1, -4, -11, -20, -31, -44, -59, -76, -95, -116, -139, -164, -191, -220, -251, -284, -319, -356, -395, -436, -479, -524, -571, -620, -671, -724, -779, -836, -895, -956, -1019, -1084, -1151, -1220, -1291, -1364, -1439, -1516, -1595, -1676, -1759, -1844, -1931, -2020, -2111, -2204, -2299, -2396, more...

integer, strictly-monotonic, +-

a(n)=5-n²
n≥0
4 operations
Power
a(n)=a(n-1)-Δ[n²]
a(0)=5
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence ytafaw0dbc4zh

5, 6, 9, 14, 21, 30, 41, 54, 69, 86, 105, 126, 149, 174, 201, 230, 261, 294, 329, 366, 405, 446, 489, 534, 581, 630, 681, 734, 789, 846, 905, 966, 1029, 1094, 1161, 1230, 1301, 1374, 1449, 1526, 1605, 1686, 1769, 1854, 1941, 2030, 2121, 2214, 2309, 2406, more...

integer, strictly-monotonic, +, A117951

a(n)=5+n²
n≥0
4 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=5
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence k2anc0tvjusxi

6, 1.5, 0.6666666666666666, 0.375, 0.24, 0.16666666666666666, 0.12244897959183673, 0.09375, 0.07407407407407407, 0.06, 0.049586776859504134, 0.041666666666666664, 0.03550295857988166, 0.030612244897959183, 0.02666666666666667, 0.0234375, 0.020761245674740483, 0.018518518518518517, 0.01662049861495845, 0.015, 0.013605442176870748, 0.012396694214876033, 0.011342155009451797, 0.010416666666666666, 0.0096, more...

decimal, strictly-monotonic, convergent, +

a(n)=6/n²
n≥1
4 operations
Power
a(n)=3/(n/(2/n))
n≥1
7 operations
Arithmetic

Sequence ngafywsvfxpek

6, 5, 2, -3, -10, -19, -30, -43, -58, -75, -94, -115, -138, -163, -190, -219, -250, -283, -318, -355, -394, -435, -478, -523, -570, -619, -670, -723, -778, -835, -894, -955, -1018, -1083, -1150, -1219, -1290, -1363, -1438, -1515, -1594, -1675, -1758, -1843, -1930, -2019, -2110, -2203, -2298, -2395, more...

integer, strictly-monotonic, +-

a(n)=6-n²
n≥0
4 operations
Power

Sequence e2nuywufrmodl

6, 7, 10, 15, 22, 31, 42, 55, 70, 87, 106, 127, 150, 175, 202, 231, 262, 295, 330, 367, 406, 447, 490, 535, 582, 631, 682, 735, 790, 847, 906, 967, 1030, 1095, 1162, 1231, 1302, 1375, 1450, 1527, 1606, 1687, 1770, 1855, 1942, 2031, 2122, 2215, 2310, 2407, more...

integer, strictly-monotonic, +, A114949

a(n)=6+n²
n≥0
4 operations
Power

Sequence a2p1ojnds4fwo

7, 1.75, 0.7777777777777778, 0.4375, 0.28, 0.19444444444444445, 0.14285714285714285, 0.109375, 0.08641975308641975, 0.07, 0.05785123966942149, 0.04861111111111111, 0.04142011834319527, 0.03571428571428571, 0.03111111111111111, 0.02734375, 0.02422145328719723, 0.021604938271604937, 0.019390581717451522, 0.0175, 0.015873015873015872, 0.014462809917355372, 0.013232514177693762, 0.012152777777777778, 0.0112, more...

decimal, strictly-monotonic, convergent, +

a(n)=7/n²
n≥1
4 operations
Power

Sequence nawwgjnjcgr0

7, 6, 3, -2, -9, -18, -29, -42, -57, -74, -93, -114, -137, -162, -189, -218, -249, -282, -317, -354, -393, -434, -477, -522, -569, -618, -669, -722, -777, -834, -893, -954, -1017, -1082, -1149, -1218, -1289, -1362, -1437, -1514, -1593, -1674, -1757, -1842, -1929, -2018, -2109, -2202, -2297, -2394, more...

integer, strictly-monotonic, +-

a(n)=7-n²
n≥0
4 operations
Power

Sequence h154rdvqvgcvm

7, 8, 11, 16, 23, 32, 43, 56, 71, 88, 107, 128, 151, 176, 203, 232, 263, 296, 331, 368, 407, 448, 491, 536, 583, 632, 683, 736, 791, 848, 907, 968, 1031, 1096, 1163, 1232, 1303, 1376, 1451, 1528, 1607, 1688, 1771, 1856, 1943, 2032, 2123, 2216, 2311, 2408, more...

integer, strictly-monotonic, +, A117619

a(n)=7+n²
n≥0
4 operations
Power

Sequence 40wwt4fncjw5d

8, 2, 0.8888888888888888, 0.5, 0.32, 0.2222222222222222, 0.16326530612244897, 0.125, 0.09876543209876543, 0.08, 0.06611570247933884, 0.05555555555555555, 0.047337278106508875, 0.04081632653061224, 0.035555555555555556, 0.03125, 0.02768166089965398, 0.024691358024691357, 0.0221606648199446, 0.02, 0.018140589569160998, 0.01652892561983471, 0.015122873345935728, 0.013888888888888888, 0.0128, more...

decimal, strictly-monotonic, convergent, +

a(n)=8/n²
n≥1
4 operations
Power

Sequence gfqelgh412dmp

8, 7, 4, -1, -8, -17, -28, -41, -56, -73, -92, -113, -136, -161, -188, -217, -248, -281, -316, -353, -392, -433, -476, -521, -568, -617, -668, -721, -776, -833, -892, -953, -1016, -1081, -1148, -1217, -1288, -1361, -1436, -1513, -1592, -1673, -1756, -1841, -1928, -2017, -2108, -2201, -2296, -2393, more...

integer, strictly-monotonic, +-

a(n)=8-n²
n≥0
4 operations
Power

Sequence x41b30xuiipgj

8, 9, 12, 17, 24, 33, 44, 57, 72, 89, 108, 129, 152, 177, 204, 233, 264, 297, 332, 369, 408, 449, 492, 537, 584, 633, 684, 737, 792, 849, 908, 969, 1032, 1097, 1164, 1233, 1304, 1377, 1452, 1529, 1608, 1689, 1772, 1857, 1944, 2033, 2124, 2217, 2312, 2409, more...

integer, strictly-monotonic, +, A189833

a(n)=8+n²
n≥0
4 operations
Power

Sequence odgp1csmu3lam

9, 2.25, 1, 0.5625, 0.36, 0.25, 0.18367346938775508, 0.140625, 0.1111111111111111, 0.09, 0.07438016528925619, 0.0625, 0.053254437869822494, 0.04591836734693877, 0.04000000000000001, 0.03515625, 0.031141868512110732, 0.027777777777777776, 0.02493074792243767, 0.0225, 0.02040816326530612, 0.018595041322314047, 0.017013232514177693, 0.015625, 0.0144, more...

decimal, strictly-monotonic, convergent, +

a(n)=(3/n)²
n≥1
4 operations
Power
a(n)=(3/(n*λ(n)))²
λ(n)=Liouville's function
n≥1
7 operations
Prime
a(n)=(τ(p(n)²)/n)²
p(n)=nth prime
τ(n)=number of divisors of n
n≥1
7 operations
Prime

Sequence 2hsx2cxpi1rud

9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, more...

integer, non-monotonic, +

a(n)=(3-n)²
n≥0
4 operations
Power

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