Sequence Database

A database with 734481 machine generated integer and decimal sequences.

Displaying result 0-99 of total 121725. [0] [1] [2] [3] [4] ... [1217]

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 esxf5io4pqwcl

-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, 1954.8584073464, 2432.8584073464, 3006.8584073464, 3714.8584073464, 4561.8584073464, 5600.8584073464, 6838.8584073464, 8345.8584073464, 10139.8584073464, 12306.8584073464, 14879.8584073464, 17973.8584073464, 21633.8584073464, 26011.8584073464, 31181.8584073464, 37334.8584073464, 44579.8584073464, 53170.8584073464, 63257.8584073464, 75171.8584073464, 89130.8584073464, 105554.8584073464, 124750.8584073464, 147269.8584073464, 173521.8584073464, 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 tl5vtjjpjnm4f

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, 195.8, 243.6, 301, 371.8, 456.5, 560.4, 684.2, 834.9, 1014.3, 1231, 1488.3, 1797.7, 2163.7, 2601.5, 3118.5, 3733.8, 4458.3, 5317.4, 6326.1, 7517.5, 8913.4, 10555.8, 12475.4, 14727.3, 17352.5, more...

decimal, monotonic, +

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

Sequence rmqkgmhztbm5f

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, 217.5555555556, 270.6666666667, 334.4444444444, 413.1111111111, 507.2222222222, 622.6666666667, 760.2222222222, 927.6666666667, 1127, 1367.7777777778, 1653.6666666667, 1997.4444444444, 2404.1111111111, 2890.5555555556, 3465, 4148.6666666667, 4953.6666666667, 5908.2222222222, 7029, 8352.7777777778, 9903.7777777778, 11728.6666666667, 13861.5555555556, 16363.6666666667, 19280.5555555556, more...

decimal, monotonic, +

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

Sequence benzwsjmkolmb

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, 244.75, 304.5, 376.25, 464.75, 570.625, 700.5, 855.25, 1043.625, 1267.875, 1538.75, 1860.375, 2247.125, 2704.625, 3251.875, 3898.125, 4667.25, 5572.875, 6646.75, 7907.625, 9396.875, 11141.75, 13194.75, 15594.25, 18409.125, 21690.625, more...

decimal, monotonic, +

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

Sequence eqkh32beovf2f

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, 279.7142857143, 348, 430, 531.1428571429, 652.1428571429, 800.5714285714, 977.4285714286, 1192.7142857143, 1449, 1758.5714285714, 2126.1428571429, 2568.1428571429, 3091, 3716.4285714286, 4455, 5334, 6369, 7596.2857142857, 9037.2857142857, 10739.2857142857, 12733.4285714286, 15079.7142857143, 17822, 21039, 24789.2857142857, more...

decimal, monotonic, +

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

Sequence y4qviwirg2b3

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, 326.3333333333, 406, 501.6666666667, 619.6666666667, 760.8333333333, 934, 1140.3333333333, 1391.5, 1690.5, 2051.6666666667, 2480.5, 2996.1666666667, 3606.1666666667, 4335.8333333333, 5197.5, 6223, 7430.5, 8862.3333333333, 10543.5, 12529.1666666667, 14855.6666666667, 17593, 20792.3333333333, 24545.5, 28920.8333333333, more...

decimal, monotonic, +

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

Sequence tjff3t0lljqxp

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, 391.6, 487.2, 602, 743.6, 913, 1120.8, 1368.4, 1669.8, 2028.6, 2462, 2976.6, 3595.4, 4327.4, 5203, 6237, 7467.6, 8916.6, 10634.8, 12652.2, 15035, 17826.8, 21111.6, 24950.8, 29454.6, 34705, more...

decimal, monotonic, +

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

Sequence 4t02pr02fcypb

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, 489.5, 609, 752.5, 929.5, 1141.25, 1401, 1710.5, 2087.25, 2535.75, 3077.5, 3720.75, 4494.25, 5409.25, 6503.75, 7796.25, 9334.5, 11145.75, 13293.5, 15815.25, 18793.75, 22283.5, 26389.5, 31188.5, 36818.25, 43381.25, more...

decimal, monotonic, +

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

Sequence ptwb3ochdoizh

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, 623.2507571479, 775.4028827437, 958.1127574132, 1183.4761568313, 1453.084630429, 1783.808602174, 2177.8762412695, 2657.5692397485, 3228.6171755622, 3918.3946989225, 4737.4060360734, 5722.256823926, 6887.2710073587, 8280.8316890713, 9926.4938006415, 11885.0545303304, 14191.2096557319, 16925.8098879369, 20136.6017098728, 23928.9456938665, 28372.233395106, 33600.1549657886, 39710.4315409726, 46878.4518679454, 55234.7230000423, more...

decimal, monotonic, +

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

Sequence 0cuk5u05stned

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, 652.6666666667, 812, 1003.3333333333, 1239.3333333333, 1521.6666666667, 1868, 2280.6666666667, 2783, 3381, 4103.3333333333, 4961, 5992.3333333333, 7212.3333333333, 8671.6666666667, 10395, 12446, 14861, 17724.6666666667, 21087, 25058.3333333333, 29711.3333333333, 35186, 41584.6666666667, 49091, 57841.6666666667, more...

decimal, monotonic, +

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

Sequence vkrryw4mswhkn

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, 979, 1218, 1505, 1859, 2282.5, 2802, 3421, 4174.5, 5071.5, 6155, 7441.5, 8988.5, 10818.5, 13007.5, 15592.5, 18669, 22291.5, 26587, 31630.5, 37587.5, 44567, 52779, 62377, 73636.5, 86762.5, 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 n0rdzulrjqafi

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, 0.0005107252, 0.000410509, 0.0003322259, 0.0002689618, 0.0002190581, 0.000178444, 0.0001461561, 0.0001197748, 0.0000985902, 0.0000812348, 0.0000671908, 0.0000556266, 0.0000462171, 0.0000384394, 0.0000320667, 0.0000267824, 0.0000224301, 0.0000188062, 0.0000158075, 0.0000133023, 0.0000112191, 0.0000094735, 0.0000080158, 0.0000067901, 0.0000057629, 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

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 k5quu0wp03g4b

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, 0.0010214505, 0.0008210181, 0.0006644518, 0.0005379236, 0.0004381161, 0.0003568879, 0.0002923122, 0.0002395496, 0.0001971803, 0.0001624695, 0.0001343815, 0.0001112533, 0.0000924343, 0.0000768787, 0.0000641334, 0.0000535647, 0.0000448601, 0.0000376124, 0.0000316151, 0.0000266046, 0.0000224381, 0.0000189469, 0.0000160316, 0.0000135802, 0.0000115257, 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 3nbye5vx4zwbb

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, -1954.8584073464, -2432.8584073464, -3006.8584073464, -3714.8584073464, -4561.8584073464, -5600.8584073464, -6838.8584073464, -8345.8584073464, -10139.8584073464, -12306.8584073464, -14879.8584073464, -17973.8584073464, -21633.8584073464, -26011.8584073464, -31181.8584073464, -37334.8584073464, -44579.8584073464, -53170.8584073464, -63257.8584073464, -75171.8584073464, -89130.8584073464, -105554.8584073464, -124750.8584073464, -147269.8584073464, -173521.8584073464, more...

decimal, monotonic, +-

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

Sequence 0syunzlltyk3h

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, 0.0015321757, 0.0012315271, 0.0009966777, 0.0008068854, 0.0006571742, 0.0005353319, 0.0004384683, 0.0003593245, 0.0002957705, 0.0002437043, 0.0002015723, 0.0001668799, 0.0001386514, 0.0001153181, 0.0000962001, 0.0000803471, 0.0000672902, 0.0000564186, 0.0000474226, 0.0000399069, 0.0000336572, 0.0000284204, 0.0000240473, 0.0000203703, 0.0000172886, 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 3zpy3gykpjwtb

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, 0.0016044906, 0.0012896522, 0.0010437185, 0.0008449684, 0.0006881912, 0.0005605983, 0.0004591629, 0.0003762837, 0.0003097301, 0.0002552066, 0.000211086, 0.0001747562, 0.0001451954, 0.0001207608, 0.0001007405, 0.0000841393, 0.0000704662, 0.0000590814, 0.0000496608, 0.0000417904, 0.0000352457, 0.0000297618, 0.0000251823, 0.0000213318, 0.0000181046, more...

decimal, monotonic, +

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

Sequence yo1jl3ie3gusd

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, 6151.2384157288, 7652.9197041447, 9456.1938873053, 11680.4414860469, 14341.3704636374, 17605.4852307172, 21494.7769358614, 26229.1570648212, 31865.1742853613, 38673.0055656904, 46756.3234633769, 56476.4111335837, 67974.6402457224, 81728.5328831385, 97970.5669021977, 117300.7864997357, 140061.6252749937, 167051.0477619836, 198740.2928587439, 236169.2277336127, 280022.7195850726, 331620.2373276314, 391926.2499059411, 462671.7748721296, 545144.8652141688, more...

decimal, monotonic, +

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

Sequence pqjt3s3eekrgj

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, 0.0020429009, 0.0016420361, 0.0013289037, 0.0010758472, 0.0008762322, 0.0007137759, 0.0005846244, 0.0004790993, 0.0003943606, 0.0003249391, 0.000268763, 0.0002225065, 0.0001848685, 0.0001537574, 0.0001282668, 0.0001071295, 0.0000897203, 0.0000752247, 0.0000632301, 0.0000532092, 0.0000448763, 0.0000378939, 0.0000320631, 0.0000271604, 0.0000230514, 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 z0canax3kmk5m

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, 1961.1415926536, 2439.1415926536, 3013.1415926536, 3721.1415926536, 4568.1415926536, 5607.1415926536, 6845.1415926536, 8352.1415926536, 10146.1415926536, 12313.1415926536, 14886.1415926536, 17980.1415926536, 21640.1415926536, 26018.1415926536, 31188.1415926536, 37341.1415926536, 44586.1415926536, 53177.1415926536, 63264.1415926536, 75178.1415926536, 89137.1415926536, 105561.1415926536, 124757.1415926536, 147276.1415926536, 173528.1415926536, more...

decimal, monotonic, +

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

Sequence 1rg2pay53woli

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, 0.0025536261, 0.0020525452, 0.0016611296, 0.001344809, 0.0010952903, 0.0008922198, 0.0007307805, 0.0005988741, 0.0004929508, 0.0004061738, 0.0003359538, 0.0002781332, 0.0002310856, 0.0001921968, 0.0001603335, 0.0001339118, 0.0001121504, 0.0000940309, 0.0000790376, 0.0000665115, 0.0000560953, 0.0000473673, 0.0000400789, 0.0000339506, 0.0000288143, 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 p5guftvyqiw4f

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, 0.0030643514, 0.0024630542, 0.0019933555, 0.0016137708, 0.0013143483, 0.0010706638, 0.0008769366, 0.0007186489, 0.000591541, 0.0004874086, 0.0004031445, 0.0003337598, 0.0002773028, 0.0002306362, 0.0001924002, 0.0001606942, 0.0001345804, 0.0001128371, 0.0000948452, 0.0000798138, 0.0000673144, 0.0000568408, 0.0000480947, 0.0000407407, 0.0000345772, 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 y2i4uil5ltrsi

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, 0.0035750766, 0.0028735632, 0.0023255814, 0.0018827327, 0.0015334064, 0.0012491078, 0.0010230927, 0.0008384238, 0.0006901311, 0.0005686434, 0.0004703353, 0.0003893864, 0.0003235199, 0.0002690755, 0.0002244669, 0.0001874766, 0.0001570105, 0.0001316433, 0.0001106527, 0.0000931161, 0.0000785334, 0.0000663143, 0.0000561104, 0.0000475308, 0.00004034, 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 rsugkwgyftxwh

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, 0.0040858018, 0.0032840722, 0.0026578073, 0.0021516945, 0.0017524644, 0.0014275517, 0.0011692488, 0.0009581986, 0.0007887213, 0.0006498781, 0.000537526, 0.0004450131, 0.000369737, 0.0003075149, 0.0002565336, 0.0002142589, 0.0001794406, 0.0001504495, 0.0001264602, 0.0001064184, 0.0000897525, 0.0000757877, 0.0000641262, 0.0000543209, 0.0000461029, 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 ipm4v3autldmi

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, 0.0045965271, 0.0036945813, 0.0029900332, 0.0024206563, 0.0019715225, 0.0016059957, 0.0013154049, 0.0010779734, 0.0008873114, 0.0007311129, 0.0006047168, 0.0005006397, 0.0004159542, 0.0003459543, 0.0002886003, 0.0002410413, 0.0002018707, 0.0001692557, 0.0001422677, 0.0001197207, 0.0001009716, 0.0000852612, 0.000072142, 0.000061111, 0.0000518657, 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 h2xxcfqol01lm

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, 0.0051072523, 0.0041050903, 0.0033222591, 0.0026896181, 0.0021905805, 0.0017844397, 0.0014615609, 0.0011977482, 0.0009859016, 0.0008123477, 0.0006719075, 0.0005562663, 0.0004621713, 0.0003843936, 0.000320667, 0.0002678237, 0.0002243007, 0.0001880618, 0.0001580753, 0.0001330229, 0.0001121906, 0.0000947346, 0.0000801578, 0.0000679011, 0.0000576286, 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(n)=characteristic function (in range)
n≥0
3 operations
Combinatoric

Sequence u4qofq5lnawde

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, more...

integer, strictly-monotonic, +, A167376

a(n)=comp(P(n))
P(n)=Partition numbers
comp(n)=complement function (in range)
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 bwyvg5rz3hhoe

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, 0.0127681307, 0.0106732348, 0.0089700997, 0.0075309306, 0.0063526835, 0.0053533191, 0.0045308389, 0.0038327943, 0.0032534753, 0.0027619821, 0.0023516764, 0.0020025588, 0.0017100337, 0.0014606958, 0.0012506013, 0.0010712947, 0.000919633, 0.0007898597, 0.0006797237, 0.000585301, 0.0005048579, 0.0004357794, 0.0003767414, 0.0003259253, 0.0002823801, 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

Sequence c1lql4nickzcj

1, 1, 1, 1.25, 1.4, 1.8333333333, 2.1428571429, 2.75, 3.3333333333, 4.2, 5.0909090909, 6.4166666667, 7.7692307692, 9.6428571429, 11.7333333333, 14.4375, 17.4705882353, 21.3888888889, 25.7894736842, 31.35, 37.7142857143, 45.5454545455, 54.5652173913, 65.625, 78.32, 93.6923076923, 111.4814814815, 132.7857142857, 157.4137931034, 186.8, 220.7096774194, 260.90625, 307.3636363636, 362.0588235294, 425.2285714286, 499.3611111111, 584.7837837838, 684.6052631579, 799.6153846154, 933.45, 1087.3902439024, 1266.0476190476, 1471.1860465116, 1708.5227272727, 1980.7555555556, 2294.7391304348, 2654.3404255319, 3068.1875, 3541.3265306122, 4084.52, more...

decimal, monotonic, +

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

Sequence hveo45atnuk1p

1, 2, 4, 6, 9, 12, 17, 22, 30, 39, 52, 67, 89, 114, 149, 191, 247, 314, 403, 509, 647, 813, 1024, 1278, 1599, 1983, 2462, 3037, 3746, 4594, 5634, 6873, 8381, 10176, 12344, 14918, 18013, 21674, 26053, 31224, 37378, 44624, 53216, 63304, 75219, 89179, 105604, 124801, 147321, 173574, more...

integer, strictly-monotonic, +, A133041

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

Sequence yi4eoqebrtatg

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

integer, monotonic, -

a(n)=-P(n²)
P(n)=Partition numbers
n≥0
4 operations
Combinatoric

Sequence ubqglrmlwilnl

-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, -

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

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