Sequence Database

A database with 1693109 machine generated integer and decimal sequences.

Displaying result 0-99 of total 159982. [0] [1] [2] [3] [4] ... [1599]

Sequence dps4an1f0bv5f

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

Sequence r2kq2q2e4g3ph

-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 x2br4y4hod3wn

-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 dfkcg1y0cnsif

-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 of2tr0wklstbd

-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 0mq1snytd5s4

-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 i3qxbl2byrve

-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 2rclvx3ggrh2n

-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 ajyjlorb1wmup

-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 1e4tr4g1t12gk

-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 doz23ccqvlupn

-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 x2k0ue53dm3me

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 hwz12ospcif4b

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 dyntzpls444jl

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 gezyjxp05uwih

0.1111111111111111, 0.1111111111111111, 0.2222222222222222, 0.3333333333333333, 0.5555555555555556, 0.7777777777777778, 1.2222222222222223, 1.6666666666666667, 2.4444444444444446, 3.3333333333333335, 4.666666666666667, 6.222222222222222, 8.555555555555555, 11.222222222222221, 15, 19.555555555555557, 25.666666666666668, 33, 42.77777777777778, 54.44444444444444, 69.66666666666667, 88, 111.33333333333333, 139.44444444444446, 175, more...

decimal, monotonic, +

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

Sequence xpqza532fhjpj

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 n2wqchgmz5zle

0.14285714285714285, 0.14285714285714285, 0.2857142857142857, 0.42857142857142855, 0.7142857142857143, 1, 1.5714285714285714, 2.142857142857143, 3.142857142857143, 4.285714285714286, 6, 8, 11, 14.428571428571429, 19.285714285714285, 25.142857142857142, 33, 42.42857142857143, 55, 70, 89.57142857142857, 113.14285714285714, 143.14285714285714, 179.28571428571428, 225, more...

decimal, monotonic, +

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

Sequence hwh5uzzgvq01o

0.16666666666666666, 0.16666666666666666, 0.3333333333333333, 0.5, 0.8333333333333334, 1.1666666666666667, 1.8333333333333333, 2.5, 3.6666666666666665, 5, 7, 9.333333333333334, 12.833333333333334, 16.833333333333332, 22.5, 29.333333333333332, 38.5, 49.5, 64.16666666666667, 81.66666666666667, 104.5, 132, 167, 209.16666666666666, 262.5, more...

decimal, monotonic, +

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

Sequence zxxvsaxl45kck

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 dbu1bwf0f24tk

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 aamimra2kaejj

0.3333333333333333, 0.3333333333333333, 0.6666666666666666, 1, 1.6666666666666667, 2.3333333333333335, 3.6666666666666665, 5, 7.333333333333333, 10, 14, 18.666666666666668, 25.666666666666668, 33.666666666666664, 45, 58.666666666666664, 77, 99, 128.33333333333334, 163.33333333333334, 209, 264, 334, 418.3333333333333, 525, more...

decimal, monotonic, +

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

Sequence zhagxgqzuljhf

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 jz2di1oytgakg

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 rr2g5wao4khwm

1, 1, 0.5, 0.3333333333333333, 0.2, 0.14285714285714285, 0.09090909090909091, 0.06666666666666667, 0.045454545454545456, 0.03333333333333333, 0.023809523809523808, 0.017857142857142856, 0.012987012987012988, 0.009900990099009901, 0.007407407407407408, 0.005681818181818182, 0.004329004329004329, 0.003367003367003367, 0.002597402597402597, 0.002040816326530612, 0.001594896331738437, 0.001262626262626263, 0.000998003992015968, 0.000796812749003984, 0.000634920634920635, more...

decimal, monotonic, convergent, +

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

Sequence jbgbpbdmticdd

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)=gcd(μ(n²), P(n))
μ(n)=Möbius function
P(n)=partition numbers
gcd(a,b)=greatest common divisor
n≥1
6 operations
Prime
a(n)=P(n)%P(p(n))
P(n)=partition numbers
p(n)=nth prime
n≥1
6 operations
Prime
a(n)=n%gpf(n)+P(n)
gpf(n)=greatest prime factor of n
P(n)=partition numbers
n≥1
7 operations
Prime

Sequence wg54b43c35omf

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 zylehz3m1x0md

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 hkvi1ekyooplj

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, 107438159466, 156919475295, 228204732751, 330495499613, 476715857290, 684957390936, 980462880430, 1398341745571, 1987276856363, 2814570987591, more...

integer, strictly-monotonic, +

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

Sequence nxt1z5dxp5iee

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, 107438159466, 172389800255, 274768617130, 435157697830, 684957390936, 1071823774337, 1667727404093, 2580840212973, 3972999029388, 6085253859260, 9275102575355, 14070545699287, 21248279009367, 31946390696157, 47826239745920, 71304185514919, 105882246722733, 156618412527946, more...

integer, strictly-monotonic, +

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

Sequence otq2a2pivxpip

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, 129913904637, 228204732751, 397125074750, 684957390936, 1171432692373, 1987276856363, 3345365983698, 5590088317495, 9275102575355, 15285151248481, 25025873760111, 40718063627362, 65851585970275, 105882246722733, 169296722391554, 269232701252579, 425933084409356, 670448123060170, 1050197489931117, 1637293969337171, 2540952590045698, 3925922161489422, more...

integer, strictly-monotonic, +

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

Sequence uhzfbpkb00ihe

1, 15, 135, 792, 3718, 14883, 53174, 173525, 526823, 1505499, 4087968, 10619863, 26543660, 64112359, 150198136, 342325709, 761002156, 1653668665, 3519222692, 7346629512, 15065878135, 30388671978, 60356673280, 118159068427, 228204732751, 435157697830, 819876908323, 1527273599625, 2814570987591, 5134205287973, 9275102575355, 16601598107914, 29454549941750, 51820051838712, 90436839668817, 156618412527946, 269232701252579, 459545750448675, 779050629562167, 1312051800816215, 2195786311682516, 3652430836071053, more...

integer, strictly-monotonic, +

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

Sequence f1wjqueinxio

1, 22, 231, 1575, 8349, 37338, 147273, 526823, 1741630, 5392783, 15796476, 44108109, 118114304, 304801365, 761002156, 1844349560, 4351078600, 10015581680, 22540654445, 49686288421, 107438159466, 228204732751, 476715857290, 980462880430, 1987276856363, 3972999029388, 7840656226137, 15285151248481, 29454549941750, 56138148670947, 105882246722733, 197726516681672, 365749566870782, 670448123060170, 1218374349844333, 2195786311682516, 3925922161489422, more...

integer, strictly-monotonic, +

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

Sequence 0byfzv1yg5u0h

1, 30, 385, 3010, 17977, 89134, 386155, 1505499, 5392783, 18004327, 56634173, 169229875, 483502844, 1327710076, 3519222692, 9035836076, 22540654445, 54770336324, 129913904637, 301384802048, 684957390936, 1527273599625, 3345365983698, 7206841706490, 15285151248481, 31946390696157, 65851585970275, 133978259344888, 269232701252579, 534715062908609, 1050197489931117, 2040825852575075, 3925922161489422, more...

integer, strictly-monotonic, +

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

Sequence 05whmxtd2kpmb

1, 42, 627, 5604, 37338, 204226, 966467, 4087968, 15796476, 56634173, 190569292, 607163746, 1844349560, 5371315400, 15065878135, 40853235313, 107438159466, 274768617130, 684957390936, 1667727404093, 3972999029388, 9275102575355, 21248279009367, 47826239745920, 105882246722733, 230793554364681, 495741934760846, 1050197489931117, 2195786311682516, more...

integer, strictly-monotonic, +

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

Sequence qn44un5nsbrhl

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 q3zpd1q211sv

2, 2, 1, 0.6666666666666666, 0.4, 0.2857142857142857, 0.18181818181818182, 0.13333333333333333, 0.09090909090909091, 0.06666666666666667, 0.047619047619047616, 0.03571428571428571, 0.025974025974025976, 0.019801980198019802, 0.014814814814814815, 0.011363636363636364, 0.008658008658008658, 0.006734006734006734, 0.005194805194805195, 0.004081632653061225, 0.003189792663476874, 0.002525252525252525, 0.001996007984031936, 0.001593625498007968, 0.00126984126984127, more...

decimal, monotonic, convergent, +

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

Sequence 1q41jr0lribap

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 vpb4h1bqvv50m

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 deoribz4budup

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 sfi5a04040nh

3, 3, 1.5, 1, 0.6, 0.42857142857142855, 0.2727272727272727, 0.2, 0.13636363636363635, 0.1, 0.07142857142857142, 0.05357142857142857, 0.03896103896103896, 0.0297029702970297, 0.022222222222222223, 0.017045454545454544, 0.012987012987012988, 0.010101010101010102, 0.007792207792207792, 0.006122448979591836, 0.004784688995215311, 0.003787878787878788, 0.002994011976047904, 0.002390438247011952, 0.001904761904761905, more...

decimal, monotonic, convergent, +

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

Sequence r5cai4wb3wsvj

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 cbmfusk0jm3cg

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 ze4sjdn4tu1vl

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, +, A299473

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

Sequence csyy055i3ibco

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 yn1qwqn5rkmlg

4, 4, 2, 1.3333333333333333, 0.8, 0.5714285714285714, 0.36363636363636365, 0.26666666666666666, 0.18181818181818182, 0.13333333333333333, 0.09523809523809523, 0.07142857142857142, 0.05194805194805195, 0.039603960396039604, 0.02962962962962963, 0.022727272727272728, 0.017316017316017316, 0.013468013468013467, 0.01038961038961039, 0.00816326530612245, 0.006379585326953748, 0.005050505050505051, 0.003992015968063872, 0.003187250996015936, 0.00253968253968254, more...

decimal, monotonic, convergent, +

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

Sequence zxmvidhtd2rmj

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 kwfbjujdcyk5m

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 xouiljjqf23fc

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, +, A299474

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

Sequence wf4tkgfphwgoe

5, 5, 2.5, 1.6666666666666667, 1, 0.7142857142857143, 0.45454545454545453, 0.3333333333333333, 0.22727272727272727, 0.16666666666666666, 0.11904761904761904, 0.08928571428571429, 0.06493506493506493, 0.04950495049504951, 0.037037037037037035, 0.028409090909090908, 0.021645021645021644, 0.016835016835016835, 0.012987012987012988, 0.01020408163265306, 0.007974481658692184, 0.006313131313131313, 0.00499001996007984, 0.00398406374501992, 0.003174603174603175, more...

decimal, monotonic, convergent, +

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

Sequence zylyxckbmvjud

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 14zmsdfefy45l

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 shgqxgum0go5m

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 yxvkxqj0lu2l

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 fphywbnv1eluh

6, 6, 3, 2, 1.2, 0.8571428571428571, 0.5454545454545454, 0.4, 0.2727272727272727, 0.2, 0.14285714285714285, 0.10714285714285714, 0.07792207792207792, 0.0594059405940594, 0.044444444444444446, 0.03409090909090909, 0.025974025974025976, 0.020202020202020204, 0.015584415584415584, 0.012244897959183673, 0.009569377990430622, 0.007575757575757576, 0.005988023952095809, 0.004780876494023904, 0.00380952380952381, more...

decimal, monotonic, convergent, +

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

Sequence le4xcaikd3oic

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 b3nifwiuhtrtm

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 t21u1dgo0zcsc

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 fbshbzpztbjmn

7, 7, 3.5, 2.3333333333333335, 1.4, 1, 0.6363636363636364, 0.4666666666666667, 0.3181818181818182, 0.23333333333333334, 0.16666666666666666, 0.125, 0.09090909090909091, 0.06930693069306931, 0.05185185185185185, 0.03977272727272727, 0.030303030303030304, 0.02356902356902357, 0.01818181818181818, 0.014285714285714285, 0.011164274322169059, 0.008838383838383838, 0.006986027944111776, 0.005577689243027889, 0.004444444444444444, more...

decimal, monotonic, convergent, +

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

Sequence cjcksnhn01pcc

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 355ajfx3kr25b

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 fp0pfdsxaopt

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 k41ilkvlzhrmj

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 r5scpa1i2geph

8, 8, 4, 2.6666666666666665, 1.6, 1.1428571428571428, 0.7272727272727273, 0.5333333333333333, 0.36363636363636365, 0.26666666666666666, 0.19047619047619047, 0.14285714285714285, 0.1038961038961039, 0.07920792079207921, 0.05925925925925926, 0.045454545454545456, 0.03463203463203463, 0.026936026936026935, 0.02077922077922078, 0.0163265306122449, 0.012759170653907496, 0.010101010101010102, 0.007984031936127744, 0.006374501992031873, 0.005079365079365079, more...

decimal, monotonic, convergent, +

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

Sequence ui4tcbercqjmf

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 rqpkhv34et35e

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 at31jhgrrn0zf

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 xnd53c5obolwo

9, 9, 4.5, 3, 1.8, 1.2857142857142858, 0.8181818181818182, 0.6, 0.4090909090909091, 0.3, 0.21428571428571427, 0.16071428571428573, 0.11688311688311688, 0.0891089108910891, 0.06666666666666667, 0.05113636363636364, 0.03896103896103896, 0.030303030303030304, 0.023376623376623377, 0.018367346938775512, 0.014354066985645933, 0.011363636363636364, 0.008982035928143712, 0.007171314741035857, 0.005714285714285714, more...

decimal, monotonic, convergent, +

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

Sequence idumgd2aecjwf

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 c330p0nshi4zc

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 gz1l5smpd5a2c

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 frpnoqs5ud5ti

10, 10, 5, 3.3333333333333335, 2, 1.4285714285714286, 0.9090909090909091, 0.6666666666666666, 0.45454545454545453, 0.3333333333333333, 0.23809523809523808, 0.17857142857142858, 0.12987012987012986, 0.09900990099009901, 0.07407407407407407, 0.056818181818181816, 0.04329004329004329, 0.03367003367003367, 0.025974025974025976, 0.02040816326530612, 0.01594896331738437, 0.012626262626262626, 0.00998003992015968, 0.00796812749003984, 0.006349206349206349, more...

decimal, monotonic, convergent, +

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

Sequence a1gapwg0djvee

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 lihmn0opy3xgp

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 ohvuusvw2olxf

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 0c2ogksyiew2m

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 w5jkgauz1bawk

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 2cj0biwgta1oe

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 mvxhv5ugifk4g

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 v2sv4zqatlxye

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 p1qn4lr4neaab

-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 0kxhfppjtpvpc

0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 8, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 8, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 8, 0, more...

integer, non-monotonic, +

a(n)=and(8, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence fowleiijym3he

0, 0, 0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 4, more...

integer, non-monotonic, +

a(n)=and(4, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence myzib3diduzno

0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, more...

integer, non-monotonic, +

a(n)=and(2, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence sgmrwgdnjcn3g

0, 0, 2, 2, 0, 2, 10, 10, 2, 10, 10, 8, 8, 0, 2, 0, 2, 8, 0, 10, 2, 8, 10, 2, 2, 2, 0, 2, 2, 0, 0, 10, 8, 10, 2, 2, 8, 0, 10, 0, 10, 2, 2, 8, 2, 10, 2, 2, 8, 0, more...

integer, non-monotonic, +

a(n)=and(10, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence yuzgni4guse5j

0, 0, 2, 2, 4, 6, 2, 6, 6, 6, 2, 0, 4, 4, 6, 0, 6, 0, 0, 2, 2, 0, 2, 6, 6, 6, 4, 2, 6, 4, 4, 2, 4, 6, 6, 2, 0, 4, 6, 0, 2, 6, 6, 4, 6, 6, 6, 2, 0, 4, more...

integer, non-monotonic, +

a(n)=and(6, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence u0znqckva2buf

0, 0, 3, 2, 4, 6, 10, 14, 23, 31, 43, 57, 76, 100, 134, 177, 230, 296, 384, 491, 626, 793, 1003, 1254, 1574, 1959, 2437, 3011, 3719, 4564, 5605, 6843, 8348, 10142, 12311, 14882, 17976, 21636, 26014, 31184, 37339, 44582, 53175, 63260, 75174, 89135, 105559, 124755, 147272, 173524, more...

integer, non-monotonic, +

a(n)=xor(1, P(n))
P(n)=partition numbers
xor(a,b)=bitwise exclusive or
n≥0
4 operations
Combinatoric

Sequence 35kf3v02nwnam

0, 1, 1, 1, 0.8, 0.7142857142857143, 0.5454545454545454, 0.4666666666666667, 0.36363636363636365, 0.3, 0.23809523809523808, 0.19642857142857142, 0.15584415584415584, 0.12871287128712872, 0.1037037037037037, 0.08522727272727272, 0.06926406926406926, 0.05723905723905724, 0.046753246753246755, 0.03877551020408163, 0.03189792663476874, 0.026515151515151516, 0.021956087824351298, 0.018326693227091632, 0.015238095238095238, more...

decimal, non-monotonic, convergent, +

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

Sequence xdy0pxypry5df

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 e1ok0u1oda2jj

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 p2pklclag21dc

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

integer, non-monotonic, +, A040051

a(n)=and(1, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric
a(n)=P(n)%2
P(n)=partition numbers
n≥0
4 operations
Combinatoric
a(n)=μ(gcd(P(n), 2)²)
P(n)=partition numbers
gcd(a,b)=greatest common divisor
μ(n)=Möbius function
n≥0
6 operations
Prime
a(n)=P(n)%p(P(a(n-1)))
a(0)=1
P(n)=partition numbers
p(n)=nth prime
n≥0
6 operations
Prime
a(n)=Ω(1+P(n)%2)
P(n)=partition numbers
Ω(n)=max distinct factors of n
n≥0
7 operations
Prime

Sequence drtkcwpxx1qro

1, 1, 0, 1, 1, 1, 9, 9, 0, 8, 8, 8, 9, 1, 1, 0, 1, 9, 1, 8, 1, 8, 8, 1, 1, 0, 0, 0, 0, 1, 0, 8, 9, 9, 0, 1, 9, 1, 9, 1, 8, 1, 0, 9, 1, 8, 0, 0, 9, 1, more...

integer, non-monotonic, +

a(n)=and(9, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence ap52ow1fxzp3j

1, 1, 0, 1, 5, 5, 1, 5, 4, 4, 0, 0, 5, 5, 5, 0, 5, 1, 1, 0, 1, 0, 0, 5, 5, 4, 4, 0, 4, 5, 4, 0, 5, 5, 4, 1, 1, 5, 5, 1, 0, 5, 4, 5, 5, 4, 4, 0, 1, 5, more...

integer, non-monotonic, +

a(n)=and(5, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric

Sequence slpxvgx2giekj

1, 1, 1, 1.25, 1.4, 1.8333333333333333, 2.142857142857143, 2.75, 3.3333333333333335, 4.2, 5.090909090909091, 6.416666666666667, 7.769230769230769, 9.642857142857142, 11.733333333333333, 14.4375, 17.470588235294116, 21.38888888888889, 25.789473684210527, 31.35, 37.714285714285715, 45.54545454545455, 54.56521739130435, 65.625, 78.32, more...

decimal, monotonic, +

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

Sequence sl2vnxesuyp0m

1, 1, 2, 3, 1, 3, 3, 3, 2, 2, 2, 0, 1, 1, 3, 0, 3, 1, 1, 2, 3, 0, 2, 3, 3, 2, 0, 2, 2, 1, 0, 2, 1, 3, 2, 3, 1, 1, 3, 1, 2, 3, 2, 1, 3, 2, 2, 2, 1, 1, more...

integer, non-monotonic, +, A121062

a(n)=and(3, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric
a(n)=P(n)%4
P(n)=partition numbers
n≥0
4 operations
Combinatoric

Sequence uvj0vcaxhetqe

1, 1, 2, 3, 5, 7, 3, 7, 6, 6, 2, 0, 5, 5, 7, 0, 7, 1, 1, 2, 3, 0, 2, 7, 7, 6, 4, 2, 6, 5, 4, 2, 5, 7, 6, 3, 1, 5, 7, 1, 2, 7, 6, 5, 7, 6, 6, 2, 1, 5, more...

integer, non-monotonic, +

a(n)=and(7, P(n))
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
4 operations
Combinatoric
a(n)=P(n)%8
P(n)=partition numbers
n≥0
4 operations
Combinatoric

Sequence 5xyc4bft0ge4g

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

integer, non-monotonic, +

a(n)=P(xor(1, n))
xor(a,b)=bitwise exclusive or
P(n)=partition numbers
n≥0
4 operations
Combinatoric

Sequence i1ee2ncloxdy

1, 1, 3, 3, 5, 7, 11, 15, 23, 31, 43, 57, 77, 101, 135, 177, 231, 297, 385, 491, 627, 793, 1003, 1255, 1575, 1959, 2437, 3011, 3719, 4565, 5605, 6843, 8349, 10143, 12311, 14883, 17977, 21637, 26015, 31185, 37339, 44583, 53175, 63261, 75175, 89135, 105559, 124755, 147273, 173525, more...

integer, monotonic, +

a(n)=or(1, P(n))
P(n)=partition numbers
or(a,b)=bitwise or
n≥0
4 operations
Combinatoric

Sequence mnocdrfh3ky0m

1, 1, 3, 3, 7, 7, 15, 15, 30, 30, 56, 56, 101, 101, 176, 176, 297, 297, 490, 490, 792, 792, 1255, 1255, 1958, 1958, 3010, 3010, 4565, 4565, 6842, 6842, 10143, 10143, 14883, 14883, 21637, 21637, 31185, 31185, 44583, 44583, 63261, 63261, 89134, 89134, 124754, 124754, 173525, 173525, more...

integer, monotonic, +

a(n)=P(or(1, n))
or(a,b)=bitwise or
P(n)=partition numbers
n≥0
4 operations
Combinatoric

Sequence 4pzhuzx1jhvfe

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 kp502gch0osfl

2, 2, 1, 0, 6, 4, 8, 12, 21, 29, 41, 59, 78, 102, 132, 179, 228, 298, 386, 489, 624, 795, 1001, 1252, 1572, 1957, 2439, 3009, 3717, 4566, 5607, 6841, 8350, 10140, 12309, 14880, 17978, 21638, 26012, 31186, 37337, 44580, 53173, 63262, 75172, 89133, 105557, 124753, 147274, 173526, more...

integer, non-monotonic, +

a(n)=xor(3, P(n))
P(n)=partition numbers
xor(a,b)=bitwise exclusive or
n≥0
4 operations
Combinatoric

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