Sequence Database

A database with 899757 machine generated integer and decimal sequences.

Displaying result 0-99 of total 137719. [0] [1] [2] [3] [4] ... [1377]

Sequence zu20zaw4iq45h

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, more...

integer, monotonic, +, A000041

a(n)=P(n)
P(n)=Partition numbers
n≥0
2 operations
Combinatoric
a(n)=P(n%p(1+n))
p(n)=nth prime
P(n)=Partition numbers
n≥0
7 operations
Prime

Sequence ayvitaowqzc3k

4, 5, 7, 15, 176, more...

integer, strictly-monotonic, +, A072215

a(n)=P(a(n-1))
a(0)=4
P(n)=Partition numbers
n≥0
2 operations
Combinatoric
a(n)=P(Ω(2^a(n-1)))
a(0)=4
Ω(n)=max factorization terms
P(n)=Partition numbers
n≥0
5 operations
Prime

Sequence 3ygvn2ndhqoup

-1, -1, -2, -3, -5, -7, -11, -15, -22, -30, -42, -56, -77, -101, -135, -176, -231, -297, -385, -490, -627, -792, -1002, -1255, -1575, -1958, -2436, -3010, -3718, -4565, -5604, -6842, -8349, -10143, -12310, -14883, -17977, -21637, -26015, -31185, -37338, -44583, -53174, -63261, -75175, -89134, -105558, -124754, -147273, -173525, more...

integer, monotonic, -

a(n)=-P(n)
P(n)=Partition numbers
n≥0
3 operations
Combinatoric

Sequence izosj4rq0ps3d

1, 1, 4, 9, 25, 49, 121, 225, 484, 900, 1764, 3136, 5929, 10201, 18225, 30976, 53361, 88209, 148225, 240100, 393129, 627264, 1004004, 1575025, 2480625, 3833764, 5934096, 9060100, 13823524, 20839225, 31404816, 46812964, 69705801, 102880449, 151536100, 221503689, 323172529, 468159769, 676780225, 972504225, 1394126244, 1987643889, 2827474276, 4001954121, 5651280625, 7944869956, 11142491364, 15563560516, 21689336529, 30110925625, more...

integer, monotonic, +, A001255

a(n)=P(n)²
P(n)=Partition numbers
n≥0
3 operations
Combinatoric

Sequence dpug0tqrlrjei

1, 1, 5, 30, 231, 1958, 17977, 173525, 1741630, 18004327, 190569292, 2056148051, 22540654445, more...

integer, monotonic, +, A072213

a(n)=P(n²)
P(n)=Partition numbers
n≥0
3 operations
Combinatoric
a(n)=P(Ω(2^n)*n)
Ω(n)=max factorization terms
P(n)=Partition numbers
n≥0
7 operations
Prime

Sequence bil0c4uurezcp

1, 1, 1, 2, 1, 3, 2, 3, 1, 5, 3, 7, 2, 7, 3, 5, 1, 7, 5, 15, 3, 22, 7, 15, 2, 15, 7, 22, 3, 15, 5, 7, 1, 11, 7, 30, 5, 56, 15, 42, 3, 56, 22, 101, 7, 77, 15, 30, 2, 30, more...

integer, non-monotonic, +

a(n)=P(stern(n))
stern(n)=Stern-Brocot sequence
P(n)=Partition numbers
n≥0
3 operations
Combinatoric

Sequence 2zvmrsuljbli

1, 1, 1, 2, 3, 3, 5, 4, 5, 4, 8, 3, 17, 19, 16, 5, 24, 40, 15, 23, 56, 16, 28, 79, 84, 55, 38, 47, 71, 201, 74, 173, 154, 158, 81, 274, 337, 469, 401, 324, 418, 716, more...

integer, non-monotonic, +

a(n)=stern(P(n))
P(n)=Partition numbers
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Combinatoric

Sequence p3xhlzmgl3k3p

-9, -9, -8, -7, -5, -3, 1, 5, 12, 20, 32, 46, 67, 91, 125, 166, 221, 287, 375, 480, 617, 782, 992, 1245, 1565, 1948, 2426, 3000, 3708, 4555, 5594, 6832, 8339, 10133, 12300, 14873, 17967, 21627, 26005, 31175, 37328, 44573, 53164, 63251, 75165, 89124, 105548, 124744, 147263, 173515, more...

integer, monotonic, +-

a(n)=P(n)-10
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence j5ect4kvc3cig

-8, -8, -7, -6, -4, -2, 2, 6, 13, 21, 33, 47, 68, 92, 126, 167, 222, 288, 376, 481, 618, 783, 993, 1246, 1566, 1949, 2427, 3001, 3709, 4556, 5595, 6833, 8340, 10134, 12301, 14874, 17968, 21628, 26006, 31176, 37329, 44574, 53165, 63252, 75166, 89125, 105549, 124745, 147264, 173516, more...

integer, monotonic, +-

a(n)=P(n)-9
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 3daicmhoymoln

-7, -7, -6, -5, -3, -1, 3, 7, 14, 22, 34, 48, 69, 93, 127, 168, 223, 289, 377, 482, 619, 784, 994, 1247, 1567, 1950, 2428, 3002, 3710, 4557, 5596, 6834, 8341, 10135, 12302, 14875, 17969, 21629, 26007, 31177, 37330, 44575, 53166, 63253, 75167, 89126, 105550, 124746, 147265, 173517, more...

integer, monotonic, +-

a(n)=P(n)-8
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence vhx21ewyszqan

-6, -6, -5, -4, -2, 0, 4, 8, 15, 23, 35, 49, 70, 94, 128, 169, 224, 290, 378, 483, 620, 785, 995, 1248, 1568, 1951, 2429, 3003, 3711, 4558, 5597, 6835, 8342, 10136, 12303, 14876, 17970, 21630, 26008, 31178, 37331, 44576, 53167, 63254, 75168, 89127, 105551, 124747, 147266, 173518, more...

integer, monotonic, +-

a(n)=P(n)-7
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence spdwg5l2xht0h

-5, -5, -4, -3, -1, 1, 5, 9, 16, 24, 36, 50, 71, 95, 129, 170, 225, 291, 379, 484, 621, 786, 996, 1249, 1569, 1952, 2430, 3004, 3712, 4559, 5598, 6836, 8343, 10137, 12304, 14877, 17971, 21631, 26009, 31179, 37332, 44577, 53168, 63255, 75169, 89128, 105552, 124748, 147267, 173519, more...

integer, monotonic, +-

a(n)=P(n)-6
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence uphvfe2q4hhqd

-4, -4, -3, -2, 0, 2, 6, 10, 17, 25, 37, 51, 72, 96, 130, 171, 226, 292, 380, 485, 622, 787, 997, 1250, 1570, 1953, 2431, 3005, 3713, 4560, 5599, 6837, 8344, 10138, 12305, 14878, 17972, 21632, 26010, 31180, 37333, 44578, 53169, 63256, 75170, 89129, 105553, 124749, 147268, 173520, more...

integer, monotonic, +-

a(n)=P(n)-5
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 2ggsh4ewkze2i

-3, -3, -2, -1, 1, 3, 7, 11, 18, 26, 38, 52, 73, 97, 131, 172, 227, 293, 381, 486, 623, 788, 998, 1251, 1571, 1954, 2432, 3006, 3714, 4561, 5600, 6838, 8345, 10139, 12306, 14879, 17973, 21633, 26011, 31181, 37334, 44579, 53170, 63257, 75171, 89130, 105554, 124750, 147269, 173521, more...

integer, monotonic, +-

a(n)=P(n)-4
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence v2j421w2pci1k

-2.1415926536, -2.1415926536, -1.1415926536, -0.1415926536, 1.8584073464, 3.8584073464, 7.8584073464, 11.8584073464, 18.8584073464, 26.8584073464, 38.8584073464, 52.8584073464, 73.8584073464, 97.8584073464, 131.8584073464, 172.8584073464, 227.8584073464, 293.8584073464, 381.8584073464, 486.8584073464, 623.8584073464, 788.8584073464, 998.8584073464, 1251.8584073464, 1571.8584073464, more...

decimal, monotonic, +-

a(n)=P(n)-π
P(n)=Partition numbers
π=3.141...
n≥0
4 operations
Combinatoric

Sequence tue1meotb4tjl

-2, -2, -1, 0, 2, 4, 8, 12, 19, 27, 39, 53, 74, 98, 132, 173, 228, 294, 382, 487, 624, 789, 999, 1252, 1572, 1955, 2433, 3007, 3715, 4562, 5601, 6839, 8346, 10140, 12307, 14880, 17974, 21634, 26012, 31182, 37335, 44580, 53171, 63258, 75172, 89131, 105555, 124751, 147270, 173522, more...

integer, monotonic, +-

a(n)=P(n)-3
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ygwm4b5i5kqcm

-1, -1, 0, 1, 3, 5, 9, 13, 20, 28, 40, 54, 75, 99, 133, 174, 229, 295, 383, 488, 625, 790, 1000, 1253, 1573, 1956, 2434, 3008, 3716, 4563, 5602, 6840, 8347, 10141, 12308, 14881, 17975, 21635, 26013, 31183, 37336, 44581, 53172, 63259, 75173, 89132, 105556, 124752, 147271, 173523, more...

integer, monotonic, +-

a(n)=P(n)-2
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 2udu5u5oprilp

0, 0, -1, -2, -4, -6, -10, -14, -21, -29, -41, -55, -76, -100, -134, -175, -230, -296, -384, -489, -626, -791, -1001, -1254, -1574, -1957, -2435, -3009, -3717, -4564, -5603, -6841, -8348, -10142, -12309, -14882, -17976, -21636, -26014, -31184, -37337, -44582, -53173, -63260, -75174, -89133, -105557, -124753, -147272, -173524, more...

integer, monotonic, -

a(n)=1-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence qkpu5yflfwr2n

0, 0, 1, 2, 4, 6, 10, 14, 21, 29, 41, 55, 76, 100, 134, 175, 230, 296, 384, 489, 626, 791, 1001, 1254, 1574, 1957, 2435, 3009, 3717, 4564, 5603, 6841, 8348, 10142, 12309, 14882, 17976, 21636, 26014, 31184, 37337, 44582, 53173, 63260, 75174, 89133, 105557, 124753, 147272, 173524, more...

integer, monotonic, +, A000065

a(n)=P(n)-1
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ly354omvdfuvf

0.1, 0.1, 0.2, 0.3, 0.5, 0.7, 1.1, 1.5, 2.2, 3, 4.2, 5.6, 7.7, 10.1, 13.5, 17.6, 23.1, 29.7, 38.5, 49, 62.7, 79.2, 100.2, 125.5, 157.5, more...

decimal, monotonic, +

a(n)=P(n)/10
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence dqdusgik0mtg

0.1111111111, 0.1111111111, 0.2222222222, 0.3333333333, 0.5555555556, 0.7777777778, 1.2222222222, 1.6666666667, 2.4444444444, 3.3333333333, 4.6666666667, 6.2222222222, 8.5555555556, 11.2222222222, 15, 19.5555555556, 25.6666666667, 33, 42.7777777778, 54.4444444444, 69.6666666667, 88, 111.3333333333, 139.4444444444, 175, more...

decimal, monotonic, +

a(n)=P(n)/9
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence pix1hpyaznmxg

0.125, 0.125, 0.25, 0.375, 0.625, 0.875, 1.375, 1.875, 2.75, 3.75, 5.25, 7, 9.625, 12.625, 16.875, 22, 28.875, 37.125, 48.125, 61.25, 78.375, 99, 125.25, 156.875, 196.875, more...

decimal, monotonic, +

a(n)=P(n)/8
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence nv4oeurf2eszd

0.1428571429, 0.1428571429, 0.2857142857, 0.4285714286, 0.7142857143, 1, 1.5714285714, 2.1428571429, 3.1428571429, 4.2857142857, 6, 8, 11, 14.4285714286, 19.2857142857, 25.1428571429, 33, 42.4285714286, 55, 70, 89.5714285714, 113.1428571429, 143.1428571429, 179.2857142857, 225, more...

decimal, monotonic, +

a(n)=P(n)/7
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ljaiycncyggrk

0.1666666667, 0.1666666667, 0.3333333333, 0.5, 0.8333333333, 1.1666666667, 1.8333333333, 2.5, 3.6666666667, 5, 7, 9.3333333333, 12.8333333333, 16.8333333333, 22.5, 29.3333333333, 38.5, 49.5, 64.1666666667, 81.6666666667, 104.5, 132, 167, 209.1666666667, 262.5, more...

decimal, monotonic, +

a(n)=P(n)/6
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 1aww4oqqxnifo

0.2, 0.2, 0.4, 0.6, 1, 1.4, 2.2, 3, 4.4, 6, 8.4, 11.2, 15.4, 20.2, 27, 35.2, 46.2, 59.4, 77, 98, 125.4, 158.4, 200.4, 251, 315, more...

decimal, monotonic, +

a(n)=P(n)/5
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence jk54k1g05guxg

0.25, 0.25, 0.5, 0.75, 1.25, 1.75, 2.75, 3.75, 5.5, 7.5, 10.5, 14, 19.25, 25.25, 33.75, 44, 57.75, 74.25, 96.25, 122.5, 156.75, 198, 250.5, 313.75, 393.75, more...

decimal, monotonic, +

a(n)=P(n)/4
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 2leew43ohfyzm

0.3183098862, 0.3183098862, 0.6366197724, 0.9549296586, 1.5915494309, 2.2281692033, 3.501408748, 4.7746482928, 7.002817496, 9.5492965855, 13.3690152197, 17.8253536263, 24.5098612362, 32.1492985046, 42.9718346348, 56.0225399683, 73.5295837085, 94.5380361966, 122.5493061808, 155.9718442301, 199.5802986372, 252.1014298576, 318.9465059562, 399.4789071607, 501.3380707395, more...

decimal, monotonic, +

a(n)=P(n)/π
P(n)=Partition numbers
π=3.141...
n≥0
4 operations
Combinatoric

Sequence 2fcfkoo5lkmyg

0.3333333333, 0.3333333333, 0.6666666667, 1, 1.6666666667, 2.3333333333, 3.6666666667, 5, 7.3333333333, 10, 14, 18.6666666667, 25.6666666667, 33.6666666667, 45, 58.6666666667, 77, 99, 128.3333333333, 163.3333333333, 209, 264, 334, 418.3333333333, 525, more...

decimal, monotonic, +

a(n)=P(n)/3
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 1yqye2zfk4vxp

0.5, 0.5, 1, 1.5, 2.5, 3.5, 5.5, 7.5, 11, 15, 21, 28, 38.5, 50.5, 67.5, 88, 115.5, 148.5, 192.5, 245, 313.5, 396, 501, 627.5, 787.5, more...

decimal, monotonic, +

a(n)=P(n)/2
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ki2d3ukbq2yan

1, 1, 0, -1, -3, -5, -9, -13, -20, -28, -40, -54, -75, -99, -133, -174, -229, -295, -383, -488, -625, -790, -1000, -1253, -1573, -1956, -2434, -3008, -3716, -4563, -5602, -6840, -8347, -10141, -12308, -14881, -17975, -21635, -26013, -31183, -37336, -44581, -53172, -63259, -75173, -89132, -105556, -124752, -147271, -173523, more...

integer, monotonic, +-

a(n)=2-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence e41fs2hh4320b

1, 1, 0.5, 0.3333333333, 0.2, 0.1428571429, 0.0909090909, 0.0666666667, 0.0454545455, 0.0333333333, 0.0238095238, 0.0178571429, 0.012987013, 0.0099009901, 0.0074074074, 0.0056818182, 0.0043290043, 0.0033670034, 0.0025974026, 0.0020408163, 0.0015948963, 0.0012626263, 0.000998004, 0.0007968127, 0.0006349206, more...

decimal, monotonic, +

a(n)=1/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence sr0qlinp2zxzf

1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, more...

integer, strictly-monotonic, +

a(n)=P(1+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric
a(n)=P(n%composite(n))
composite(n)=nth composite number
P(n)=Partition numbers
n≥1
5 operations
Prime

Sequence vbnuo5tlma3vj

1, 2, 5, 11, 22, 42, 77, 135, 231, 385, 627, 1002, 1575, 2436, 3718, 5604, 8349, 12310, 17977, 26015, 37338, 53174, 75175, 105558, 147273, 204226, 281589, 386155, 526823, 715220, 966467, 1300156, 1741630, 2323520, 3087735, 4087968, 5392783, 7089500, 9289091, 12132164, 15796476, 20506255, 26543660, 34262962, 44108109, 56634173, 72533807, 92669720, 118114304, 150198136, more...

integer, strictly-monotonic, +, A058696

a(n)=P(2*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence zvb4xwbeh45pb

1, 3, 11, 30, 77, 176, 385, 792, 1575, 3010, 5604, 10143, 17977, 31185, 53174, 89134, 147273, 239943, 386155, 614154, 966467, 1505499, 2323520, 3554345, 5392783, 8118264, 12132164, 18004327, 26543660, 38887673, 56634173, 82010177, 118114304, 169229875, 241265379, 342325709, 483502844, 679903203, 952050665, 1327710076, 1844349560, 2552338241, 3519222692, 4835271870, 6620830889, 9035836076, 12292341831, 16670689208, 22540654445, 30388671978, more...

integer, strictly-monotonic, +

a(n)=P(3*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric
a(n)=P(∑(p(τ(a(n-1)))))
a(0)=1
τ(n)=number of divisors of n
p(n)=nth prime
∑(a)=partial sums of a
P(n)=Partition numbers
n≥0
5 operations
Prime

Sequence 0ywjiluwzp4mb

1, 5, 22, 77, 231, 627, 1575, 3718, 8349, 17977, 37338, 75175, 147273, 281589, 526823, 966467, 1741630, 3087735, 5392783, 9289091, 15796476, 26543660, 44108109, 72533807, 118114304, 190569292, 304801365, 483502844, 761002156, 1188908248, 1844349560, 2841940500, 4351078600, 6620830889, 10015581680, 15065878135, 22540654445, 33549419497, 49686288421, 73232243759, more...

integer, strictly-monotonic, +

a(n)=P(4*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence zjquwlskzkd1i

1, 7, 42, 176, 627, 1958, 5604, 14883, 37338, 89134, 204226, 451276, 966467, 2012558, 4087968, 8118264, 15796476, 30167357, 56634173, 104651419, 190569292, 342325709, 607163746, 1064144451, 1844349560, 3163127352, 5371315400, 9035836076, 15065878135, 24908858009, 40853235313, 66493182097, more...

integer, strictly-monotonic, +

a(n)=P(5*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence hsek1cssab3hd

1, 11, 77, 385, 1575, 5604, 17977, 53174, 147273, 386155, 966467, 2323520, 5392783, 12132164, 26543660, 56634173, 118114304, 241265379, 483502844, 952050665, 1844349560, 3519222692, 6620830889, 12292341831, 22540654445, 40853235313, 73232243759, more...

integer, strictly-monotonic, +

a(n)=P(6*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence agukqg3mzl5ej

1, 15, 135, 792, 3718, 14883, 53174, 173525, 526823, 1505499, 4087968, 10619863, 26543660, 64112359, 150198136, 342325709, 761002156, 1653668665, 3519222692, 7346629512, 15065878135, 30388671978, 60356673280, more...

integer, strictly-monotonic, +

a(n)=P(7*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 1tluyhkbiwlxm

1, 22, 231, 1575, 8349, 37338, 147273, 526823, 1741630, 5392783, 15796476, 44108109, 118114304, 304801365, 761002156, 1844349560, 4351078600, 10015581680, 22540654445, 49686288421, more...

integer, strictly-monotonic, +

a(n)=P(8*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence pu1hssiq0vf0l

1, 30, 385, 3010, 17977, 89134, 386155, 1505499, 5392783, 18004327, 56634173, 169229875, 483502844, 1327710076, 3519222692, 9035836076, 22540654445, 54770336324, more...

integer, strictly-monotonic, +

a(n)=P(9*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence n04f1stkqihmn

1, 42, 627, 5604, 37338, 204226, 966467, 4087968, 15796476, 56634173, 190569292, 607163746, 1844349560, 5371315400, 15065878135, 40853235313, more...

integer, strictly-monotonic, +

a(n)=P(10*n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence vvzb23tjkjhph

2, 2, 1, 0, -2, -4, -8, -12, -19, -27, -39, -53, -74, -98, -132, -173, -228, -294, -382, -487, -624, -789, -999, -1252, -1572, -1955, -2433, -3007, -3715, -4562, -5601, -6839, -8346, -10140, -12307, -14880, -17974, -21634, -26012, -31182, -37335, -44580, -53171, -63258, -75172, -89131, -105555, -124751, -147270, -173522, more...

integer, monotonic, +-

a(n)=3-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 32wyaov1sjq1h

2, 2, 1, 0.6666666667, 0.4, 0.2857142857, 0.1818181818, 0.1333333333, 0.0909090909, 0.0666666667, 0.0476190476, 0.0357142857, 0.025974026, 0.0198019802, 0.0148148148, 0.0113636364, 0.0086580087, 0.0067340067, 0.0051948052, 0.0040816327, 0.0031897927, 0.0025252525, 0.001996008, 0.0015936255, 0.0012698413, more...

decimal, monotonic, +

a(n)=2/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 3wyzizi4qiqll

2, 2, 3, 4, 6, 8, 12, 16, 23, 31, 43, 57, 78, 102, 136, 177, 232, 298, 386, 491, 628, 793, 1003, 1256, 1576, 1959, 2437, 3011, 3719, 4566, 5605, 6843, 8350, 10144, 12311, 14884, 17978, 21638, 26016, 31186, 37339, 44584, 53175, 63262, 75176, 89135, 105559, 124755, 147274, 173526, more...

integer, monotonic, +

a(n)=1+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence kqvg5fdpfeky

2, 2, 4, 6, 10, 14, 22, 30, 44, 60, 84, 112, 154, 202, 270, 352, 462, 594, 770, 980, 1254, 1584, 2004, 2510, 3150, 3916, 4872, 6020, 7436, 9130, 11208, 13684, 16698, 20286, 24620, 29766, 35954, 43274, 52030, 62370, 74676, 89166, 106348, 126522, 150350, 178268, 211116, 249508, 294546, 347050, more...

integer, monotonic, +, A139582

a(n)=2*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence fcxksl2h5x0ig

2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, more...

integer, strictly-monotonic, +

a(n)=P(2+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence utpak4t05esxo

2.1415926536, 2.1415926536, 1.1415926536, 0.1415926536, -1.8584073464, -3.8584073464, -7.8584073464, -11.8584073464, -18.8584073464, -26.8584073464, -38.8584073464, -52.8584073464, -73.8584073464, -97.8584073464, -131.8584073464, -172.8584073464, -227.8584073464, -293.8584073464, -381.8584073464, -486.8584073464, -623.8584073464, -788.8584073464, -998.8584073464, -1251.8584073464, -1571.8584073464, more...

decimal, monotonic, +-

a(n)=π-P(n)
π=3.141...
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ns0rmpd4244tm

3, 3, 1.5, 1, 0.6, 0.4285714286, 0.2727272727, 0.2, 0.1363636364, 0.1, 0.0714285714, 0.0535714286, 0.038961039, 0.0297029703, 0.0222222222, 0.0170454545, 0.012987013, 0.0101010101, 0.0077922078, 0.006122449, 0.004784689, 0.0037878788, 0.002994012, 0.0023904382, 0.0019047619, more...

decimal, monotonic, +

a(n)=3/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence zmrbmnczixmen

3, 3, 2, 1, -1, -3, -7, -11, -18, -26, -38, -52, -73, -97, -131, -172, -227, -293, -381, -486, -623, -788, -998, -1251, -1571, -1954, -2432, -3006, -3714, -4561, -5600, -6838, -8345, -10139, -12306, -14879, -17973, -21633, -26011, -31181, -37334, -44579, -53170, -63257, -75171, -89130, -105554, -124750, -147269, -173521, more...

integer, monotonic, +-

a(n)=4-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence n2ntfvyh3r35g

3, 3, 4, 5, 7, 9, 13, 17, 24, 32, 44, 58, 79, 103, 137, 178, 233, 299, 387, 492, 629, 794, 1004, 1257, 1577, 1960, 2438, 3012, 3720, 4567, 5606, 6844, 8351, 10145, 12312, 14885, 17979, 21639, 26017, 31187, 37340, 44585, 53176, 63263, 75177, 89136, 105560, 124756, 147275, 173527, more...

integer, monotonic, +

a(n)=2+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence r5mac1ode3s2i

3, 3, 6, 9, 15, 21, 33, 45, 66, 90, 126, 168, 231, 303, 405, 528, 693, 891, 1155, 1470, 1881, 2376, 3006, 3765, 4725, 5874, 7308, 9030, 11154, 13695, 16812, 20526, 25047, 30429, 36930, 44649, 53931, 64911, 78045, 93555, 112014, 133749, 159522, 189783, 225525, 267402, 316674, 374262, 441819, 520575, more...

integer, monotonic, +

a(n)=3*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence klygzsbdpnzjk

3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, more...

integer, strictly-monotonic, +

a(n)=P(3+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 4ekdoekp0cwce

3.1415926536, 3.1415926536, 1.5707963268, 1.0471975512, 0.6283185307, 0.4487989505, 0.2855993321, 0.2094395102, 0.1427996661, 0.1047197551, 0.0747998251, 0.0560998688, 0.0407999046, 0.0311048778, 0.0232710567, 0.0178499583, 0.0135999682, 0.010577753, 0.0081599809, 0.0064114136, 0.0050105146, 0.0039666574, 0.003135322, 0.0025032611, 0.001994662, more...

decimal, monotonic, +

a(n)=π/P(n)
π=3.141...
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence fblsf4bcan24p

3.1415926536, 3.1415926536, 6.2831853072, 9.4247779608, 15.7079632679, 21.9911485751, 34.5575191895, 47.1238898038, 69.115038379, 94.2477796077, 131.9468914508, 175.929188601, 241.9026343264, 317.3008580126, 424.1150082346, 552.9203070318, 725.7079029792, 933.0530181162, 1209.5131716321, 1539.380400259, 1969.7785938008, 2488.1413816431, 3147.875838897, 3942.6987802552, 4948.0084294039, more...

decimal, monotonic, +

a(n)=π*P(n)
π=3.141...
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence gddf13t42uggn

4, 4, 2, 1.3333333333, 0.8, 0.5714285714, 0.3636363636, 0.2666666667, 0.1818181818, 0.1333333333, 0.0952380952, 0.0714285714, 0.0519480519, 0.0396039604, 0.0296296296, 0.0227272727, 0.0173160173, 0.0134680135, 0.0103896104, 0.0081632653, 0.0063795853, 0.0050505051, 0.003992016, 0.003187251, 0.0025396825, more...

decimal, monotonic, +

a(n)=4/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence yho2t4spg51yd

4, 4, 3, 2, 0, -2, -6, -10, -17, -25, -37, -51, -72, -96, -130, -171, -226, -292, -380, -485, -622, -787, -997, -1250, -1570, -1953, -2431, -3005, -3713, -4560, -5599, -6837, -8344, -10138, -12305, -14878, -17972, -21632, -26010, -31180, -37333, -44578, -53169, -63256, -75170, -89129, -105553, -124749, -147268, -173520, more...

integer, monotonic, +-

a(n)=5-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence fyfs4rmibxuug

4, 4, 5, 6, 8, 10, 14, 18, 25, 33, 45, 59, 80, 104, 138, 179, 234, 300, 388, 493, 630, 795, 1005, 1258, 1578, 1961, 2439, 3013, 3721, 4568, 5607, 6845, 8352, 10146, 12313, 14886, 17980, 21640, 26018, 31188, 37341, 44586, 53177, 63264, 75178, 89137, 105561, 124757, 147276, 173528, more...

integer, monotonic, +

a(n)=3+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ropfe2dwd4iwc

4, 4, 8, 12, 20, 28, 44, 60, 88, 120, 168, 224, 308, 404, 540, 704, 924, 1188, 1540, 1960, 2508, 3168, 4008, 5020, 6300, 7832, 9744, 12040, 14872, 18260, 22416, 27368, 33396, 40572, 49240, 59532, 71908, 86548, 104060, 124740, 149352, 178332, 212696, 253044, 300700, 356536, 422232, 499016, 589092, 694100, more...

integer, monotonic, +

a(n)=4*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence p2kx53jcebsbo

4.1415926536, 4.1415926536, 5.1415926536, 6.1415926536, 8.1415926536, 10.1415926536, 14.1415926536, 18.1415926536, 25.1415926536, 33.1415926536, 45.1415926536, 59.1415926536, 80.1415926536, 104.1415926536, 138.1415926536, 179.1415926536, 234.1415926536, 300.1415926536, 388.1415926536, 493.1415926536, 630.1415926536, 795.1415926536, 1005.1415926536, 1258.1415926536, 1578.1415926536, more...

decimal, monotonic, +

a(n)=π+P(n)
π=3.141...
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 42okzur0y1iuh

5, 5, 2.5, 1.6666666667, 1, 0.7142857143, 0.4545454545, 0.3333333333, 0.2272727273, 0.1666666667, 0.119047619, 0.0892857143, 0.0649350649, 0.0495049505, 0.037037037, 0.0284090909, 0.0216450216, 0.0168350168, 0.012987013, 0.0102040816, 0.0079744817, 0.0063131313, 0.00499002, 0.0039840637, 0.0031746032, more...

decimal, monotonic, +

a(n)=5/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence eouc0uwnj1pyc

5, 5, 4, 3, 1, -1, -5, -9, -16, -24, -36, -50, -71, -95, -129, -170, -225, -291, -379, -484, -621, -786, -996, -1249, -1569, -1952, -2430, -3004, -3712, -4559, -5598, -6836, -8343, -10137, -12304, -14877, -17971, -21631, -26009, -31179, -37332, -44577, -53168, -63255, -75169, -89128, -105552, -124748, -147267, -173519, more...

integer, monotonic, +-

a(n)=6-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence tgvsoyp4umw5o

5, 5, 6, 7, 9, 11, 15, 19, 26, 34, 46, 60, 81, 105, 139, 180, 235, 301, 389, 494, 631, 796, 1006, 1259, 1579, 1962, 2440, 3014, 3722, 4569, 5608, 6846, 8353, 10147, 12314, 14887, 17981, 21641, 26019, 31189, 37342, 44587, 53178, 63265, 75179, 89138, 105562, 124758, 147277, 173529, more...

integer, monotonic, +

a(n)=4+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence x05qd1pjqoegb

5, 5, 10, 15, 25, 35, 55, 75, 110, 150, 210, 280, 385, 505, 675, 880, 1155, 1485, 1925, 2450, 3135, 3960, 5010, 6275, 7875, 9790, 12180, 15050, 18590, 22825, 28020, 34210, 41745, 50715, 61550, 74415, 89885, 108185, 130075, 155925, 186690, 222915, 265870, 316305, 375875, 445670, 527790, 623770, 736365, 867625, more...

integer, monotonic, +

a(n)=5*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence v10wtbinheope

5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, more...

integer, strictly-monotonic, +

a(n)=P(4+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence wfir4eneemzsk

6, 6, 3, 2, 1.2, 0.8571428571, 0.5454545455, 0.4, 0.2727272727, 0.2, 0.1428571429, 0.1071428571, 0.0779220779, 0.0594059406, 0.0444444444, 0.0340909091, 0.025974026, 0.0202020202, 0.0155844156, 0.012244898, 0.009569378, 0.0075757576, 0.005988024, 0.0047808765, 0.0038095238, more...

decimal, monotonic, +

a(n)=6/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence mgsajd4xgu0fg

6, 6, 5, 4, 2, 0, -4, -8, -15, -23, -35, -49, -70, -94, -128, -169, -224, -290, -378, -483, -620, -785, -995, -1248, -1568, -1951, -2429, -3003, -3711, -4558, -5597, -6835, -8342, -10136, -12303, -14876, -17970, -21630, -26008, -31178, -37331, -44576, -53167, -63254, -75168, -89127, -105551, -124747, -147266, -173518, more...

integer, monotonic, +-

a(n)=7-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ifje1ymq0d5ol

6, 6, 7, 8, 10, 12, 16, 20, 27, 35, 47, 61, 82, 106, 140, 181, 236, 302, 390, 495, 632, 797, 1007, 1260, 1580, 1963, 2441, 3015, 3723, 4570, 5609, 6847, 8354, 10148, 12315, 14888, 17982, 21642, 26020, 31190, 37343, 44588, 53179, 63266, 75180, 89139, 105563, 124759, 147278, 173530, more...

integer, monotonic, +

a(n)=5+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence n0jacdj5kzlvk

6, 6, 12, 18, 30, 42, 66, 90, 132, 180, 252, 336, 462, 606, 810, 1056, 1386, 1782, 2310, 2940, 3762, 4752, 6012, 7530, 9450, 11748, 14616, 18060, 22308, 27390, 33624, 41052, 50094, 60858, 73860, 89298, 107862, 129822, 156090, 187110, 224028, 267498, 319044, 379566, 451050, 534804, 633348, 748524, 883638, 1041150, more...

integer, monotonic, +

a(n)=6*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 1mep3hsz0ciei

7, 7, 3.5, 2.3333333333, 1.4, 1, 0.6363636364, 0.4666666667, 0.3181818182, 0.2333333333, 0.1666666667, 0.125, 0.0909090909, 0.0693069307, 0.0518518519, 0.0397727273, 0.0303030303, 0.0235690236, 0.0181818182, 0.0142857143, 0.0111642743, 0.0088383838, 0.0069860279, 0.0055776892, 0.0044444444, more...

decimal, monotonic, +

a(n)=7/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence i0dglhlzp50jh

7, 7, 6, 5, 3, 1, -3, -7, -14, -22, -34, -48, -69, -93, -127, -168, -223, -289, -377, -482, -619, -784, -994, -1247, -1567, -1950, -2428, -3002, -3710, -4557, -5596, -6834, -8341, -10135, -12302, -14875, -17969, -21629, -26007, -31177, -37330, -44575, -53166, -63253, -75167, -89126, -105550, -124746, -147265, -173517, more...

integer, monotonic, +-

a(n)=8-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ziuompqkm1kxk

7, 7, 8, 9, 11, 13, 17, 21, 28, 36, 48, 62, 83, 107, 141, 182, 237, 303, 391, 496, 633, 798, 1008, 1261, 1581, 1964, 2442, 3016, 3724, 4571, 5610, 6848, 8355, 10149, 12316, 14889, 17983, 21643, 26021, 31191, 37344, 44589, 53180, 63267, 75181, 89140, 105564, 124760, 147279, 173531, more...

integer, monotonic, +

a(n)=6+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence bxh11yz2q52rp

7, 7, 14, 21, 35, 49, 77, 105, 154, 210, 294, 392, 539, 707, 945, 1232, 1617, 2079, 2695, 3430, 4389, 5544, 7014, 8785, 11025, 13706, 17052, 21070, 26026, 31955, 39228, 47894, 58443, 71001, 86170, 104181, 125839, 151459, 182105, 218295, 261366, 312081, 372218, 442827, 526225, 623938, 738906, 873278, 1030911, 1214675, more...

integer, monotonic, +

a(n)=7*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ays5sxzfpsezn

7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, 386155, more...

integer, strictly-monotonic, +

a(n)=P(5+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence xkmzznsgtnkpb

8, 8, 4, 2.6666666667, 1.6, 1.1428571429, 0.7272727273, 0.5333333333, 0.3636363636, 0.2666666667, 0.1904761905, 0.1428571429, 0.1038961039, 0.0792079208, 0.0592592593, 0.0454545455, 0.0346320346, 0.0269360269, 0.0207792208, 0.0163265306, 0.0127591707, 0.0101010101, 0.0079840319, 0.006374502, 0.0050793651, more...

decimal, monotonic, +

a(n)=8/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence iyqcaqdbvqqjc

8, 8, 7, 6, 4, 2, -2, -6, -13, -21, -33, -47, -68, -92, -126, -167, -222, -288, -376, -481, -618, -783, -993, -1246, -1566, -1949, -2427, -3001, -3709, -4556, -5595, -6833, -8340, -10134, -12301, -14874, -17968, -21628, -26006, -31176, -37329, -44574, -53165, -63252, -75166, -89125, -105549, -124745, -147264, -173516, more...

integer, monotonic, +-

a(n)=9-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence jelfi22gri5ge

8, 8, 9, 10, 12, 14, 18, 22, 29, 37, 49, 63, 84, 108, 142, 183, 238, 304, 392, 497, 634, 799, 1009, 1262, 1582, 1965, 2443, 3017, 3725, 4572, 5611, 6849, 8356, 10150, 12317, 14890, 17984, 21644, 26022, 31192, 37345, 44590, 53181, 63268, 75182, 89141, 105565, 124761, 147280, 173532, more...

integer, monotonic, +

a(n)=7+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence pudzitfwimvrn

8, 8, 16, 24, 40, 56, 88, 120, 176, 240, 336, 448, 616, 808, 1080, 1408, 1848, 2376, 3080, 3920, 5016, 6336, 8016, 10040, 12600, 15664, 19488, 24080, 29744, 36520, 44832, 54736, 66792, 81144, 98480, 119064, 143816, 173096, 208120, 249480, 298704, 356664, 425392, 506088, 601400, 713072, 844464, 998032, 1178184, 1388200, more...

integer, monotonic, +

a(n)=8*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence rnzx4swxcdkvp

9, 9, 4.5, 3, 1.8, 1.2857142857, 0.8181818182, 0.6, 0.4090909091, 0.3, 0.2142857143, 0.1607142857, 0.1168831169, 0.0891089109, 0.0666666667, 0.0511363636, 0.038961039, 0.0303030303, 0.0233766234, 0.0183673469, 0.014354067, 0.0113636364, 0.0089820359, 0.0071713147, 0.0057142857, more...

decimal, monotonic, +

a(n)=9/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 50mumyedpzx5e

9, 9, 8, 7, 5, 3, -1, -5, -12, -20, -32, -46, -67, -91, -125, -166, -221, -287, -375, -480, -617, -782, -992, -1245, -1565, -1948, -2426, -3000, -3708, -4555, -5594, -6832, -8339, -10133, -12300, -14873, -17967, -21627, -26005, -31175, -37328, -44573, -53164, -63251, -75165, -89124, -105548, -124744, -147263, -173515, more...

integer, monotonic, +-

a(n)=10-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence mc1nvxmb35bup

9, 9, 10, 11, 13, 15, 19, 23, 30, 38, 50, 64, 85, 109, 143, 184, 239, 305, 393, 498, 635, 800, 1010, 1263, 1583, 1966, 2444, 3018, 3726, 4573, 5612, 6850, 8357, 10151, 12318, 14891, 17985, 21645, 26023, 31193, 37346, 44591, 53182, 63269, 75183, 89142, 105566, 124762, 147281, 173533, more...

integer, monotonic, +

a(n)=8+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence qrqnbxhecrer

9, 9, 18, 27, 45, 63, 99, 135, 198, 270, 378, 504, 693, 909, 1215, 1584, 2079, 2673, 3465, 4410, 5643, 7128, 9018, 11295, 14175, 17622, 21924, 27090, 33462, 41085, 50436, 61578, 75141, 91287, 110790, 133947, 161793, 194733, 234135, 280665, 336042, 401247, 478566, 569349, 676575, 802206, 950022, 1122786, 1325457, 1561725, more...

integer, monotonic, +

a(n)=9*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 3plqdpshalqnj

10, 10, 5, 3.3333333333, 2, 1.4285714286, 0.9090909091, 0.6666666667, 0.4545454545, 0.3333333333, 0.2380952381, 0.1785714286, 0.1298701299, 0.099009901, 0.0740740741, 0.0568181818, 0.0432900433, 0.0336700337, 0.025974026, 0.0204081633, 0.0159489633, 0.0126262626, 0.0099800399, 0.0079681275, 0.0063492063, more...

decimal, monotonic, +

a(n)=10/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence sddfxzdfolojc

10, 10, 11, 12, 14, 16, 20, 24, 31, 39, 51, 65, 86, 110, 144, 185, 240, 306, 394, 499, 636, 801, 1011, 1264, 1584, 1967, 2445, 3019, 3727, 4574, 5613, 6851, 8358, 10152, 12319, 14892, 17986, 21646, 26024, 31194, 37347, 44592, 53183, 63270, 75184, 89143, 105567, 124763, 147282, 173534, more...

integer, monotonic, +

a(n)=9+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence b5x4zj4zmmp3m

10, 10, 20, 30, 50, 70, 110, 150, 220, 300, 420, 560, 770, 1010, 1350, 1760, 2310, 2970, 3850, 4900, 6270, 7920, 10020, 12550, 15750, 19580, 24360, 30100, 37180, 45650, 56040, 68420, 83490, 101430, 123100, 148830, 179770, 216370, 260150, 311850, 373380, 445830, 531740, 632610, 751750, 891340, 1055580, 1247540, 1472730, 1735250, more...

integer, monotonic, +

a(n)=10*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ll45vvrsm5ltc

11, 11, 12, 13, 15, 17, 21, 25, 32, 40, 52, 66, 87, 111, 145, 186, 241, 307, 395, 500, 637, 802, 1012, 1265, 1585, 1968, 2446, 3020, 3728, 4575, 5614, 6852, 8359, 10153, 12320, 14893, 17987, 21647, 26025, 31195, 37348, 44593, 53184, 63271, 75185, 89144, 105568, 124764, 147283, 173535, more...

integer, monotonic, +

a(n)=10+P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence sm5a0zzz1i31h

11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, 386155, 451276, more...

integer, strictly-monotonic, +

a(n)=P(6+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 1lbriyrsg1bud

15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, 386155, 451276, 526823, more...

integer, strictly-monotonic, +

a(n)=P(7+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence h5upve5ahjwce

22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, 386155, 451276, 526823, 614154, more...

integer, strictly-monotonic, +

a(n)=P(8+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence dzjnspdlbo3o

30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, 386155, 451276, 526823, 614154, 715220, more...

integer, strictly-monotonic, +

a(n)=P(9+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence 0sobmwvmqk0lh

42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, 204226, 239943, 281589, 329931, 386155, 451276, 526823, 614154, 715220, 831820, more...

integer, strictly-monotonic, +

a(n)=P(10+n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence nh3j5hdt2ul2f

0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +, A167392

a(n)=cf(P(n))
P(n)=Partition numbers
cf(a)=characteristic function of a (in range)
n≥0
3 operations
Combinatoric
a(n)=cf(P(stern(composite(n))))
composite(n)=nth composite number
stern(n)=Stern-Brocot sequence
P(n)=Partition numbers
cf(a)=characteristic function of a (in range)
n≥1
5 operations
Prime

Sequence t3ikdd122nxzb

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 320, 383, 478, 574, 708, 847, 1039, 1238, 1507, 1794, 2167, 2573, 3094, 3660, 4378, 5170, 6153, 7245, 8591, 10087, 11914, 13959, 16424, 19196, 22519, 26252, 30701, more...

integer, monotonic, +

a(n)=Δ(P(n))
P(n)=Partition numbers
Δ(a)=differences of a
n≥0
3 operations
Combinatoric

Sequence ua31jsbis5dhg

0, 4, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, more...

integer, strictly-monotonic, +, A167376

a(n)=comp(P(n))
P(n)=Partition numbers
comp(a)=complement function of a (in range)
n≥0
3 operations
Combinatoric
a(n)=comp(P(stern(composite(n))))
composite(n)=nth composite number
stern(n)=Stern-Brocot sequence
P(n)=Partition numbers
comp(a)=complement function of a (in range)
n≥1
5 operations
Prime

Sequence pfknnfoj2ijdp

1, 1, 2, 6, 30, 210, 2310, 34650, 762300, 22869000, 960498000, 53787888000, more...

integer, monotonic, +, A058694

a(n)=∏(P(n))
P(n)=Partition numbers
∏(a)=partial products of a
n≥0
3 operations
Combinatoric

Sequence ecqgmf1yrmh5p

1, 1, 3, 11, 42, 176, 792, 3718, 17977, 89134, 451276, 2323520, 12132164, 64112359, 342325709, 1844349560, 10015581680, 54770336324, more...

integer, monotonic, +, A066655

a(n)=P(∑(n))
∑(a)=partial sums of a
P(n)=Partition numbers
n≥0
3 operations
Combinatoric

Sequence 54hv3wv5t0afb

1, 2, 4, 7, 12, 19, 30, 45, 67, 97, 139, 195, 272, 373, 508, 684, 915, 1212, 1597, 2087, 2714, 3506, 4508, 5763, 7338, 9296, 11732, 14742, 18460, 23025, 28629, 35471, 43820, 53963, 66273, 81156, 99133, 120770, 146785, 177970, 215308, 259891, 313065, 376326, 451501, 540635, 646193, 770947, 918220, 1091745, more...

integer, strictly-monotonic, +, A000070

a(n)=∑(P(n))
P(n)=Partition numbers
∑(a)=partial sums of a
n≥0
3 operations
Combinatoric

Sequence io5o2xkofxlrp

-1, 0, 0, 0, -1, -2, -5, -8, -14, -21, -32, -45, -65, -88, -121, -161, -215, -280, -367, -471, -607, -771, -980, -1232, -1551, -1933, -2410, -2983, -3690, -4536, -5574, -6811, -8317, -10110, -12276, -14848, -17941, -21600, -25977, -31146, -37298, -44542, -53132, -63218, -75131, -89089, -105512, -124707, -147225, -173476, more...

integer, non-monotonic, -

a(n)=n-P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence vulorws5v2dpn

0, 1, 1, 1, 0.8, 0.7142857143, 0.5454545455, 0.4666666667, 0.3636363636, 0.3, 0.2380952381, 0.1964285714, 0.1558441558, 0.1287128713, 0.1037037037, 0.0852272727, 0.0692640693, 0.0572390572, 0.0467532468, 0.0387755102, 0.0318979266, 0.0265151515, 0.0219560878, 0.0183266932, 0.0152380952, more...

decimal, non-monotonic, +

a(n)=n/P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence okj33cghibbil

0, 1, 4, 9, 20, 35, 66, 105, 176, 270, 420, 616, 924, 1313, 1890, 2640, 3696, 5049, 6930, 9310, 12540, 16632, 22044, 28865, 37800, 48950, 63336, 81270, 104104, 132385, 168120, 212102, 267168, 334719, 418540, 520905, 647172, 800569, 988570, 1216215, 1493520, 1827903, 2233308, 2720223, 3307700, 4011030, 4855668, 5863438, 7069104, 8502725, more...

integer, strictly-monotonic, +, A066186

a(n)=n*P(n)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence c4xz0eusjeazj

1, 0, 0, 0, 1, 2, 5, 8, 14, 21, 32, 45, 65, 88, 121, 161, 215, 280, 367, 471, 607, 771, 980, 1232, 1551, 1933, 2410, 2983, 3690, 4536, 5574, 6811, 8317, 10110, 12276, 14848, 17941, 21600, 25977, 31146, 37298, 44542, 53132, 63218, 75131, 89089, 105512, 124707, 147225, 173476, more...

integer, non-monotonic, +

a(n)=P(n)-n
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

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