A243088
Number of compositions of n into parts with multiplicity not larger than 10.
Original entry on oeis.org
1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2047, 4083, 8166, 16266, 32466, 64580, 128522, 255119, 506025, 1001545, 1979285, 3903439, 7683348, 15091124, 29577303, 57838511, 112844632, 219646810, 426513292, 826201797, 1596503761, 3077988342, 5917798459
Offset: 0
-
b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j)/j!, j=0..min(n/i, 10))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50);
A243119
Number of compositions of n in which the maximal multiplicity of parts equals 2.
Original entry on oeis.org
1, 0, 4, 6, 10, 21, 40, 87, 121, 219, 421, 690, 1159, 1782, 3304, 5190, 8212, 12897, 22084, 33255, 53617, 82539, 124849, 206172, 313339, 472056, 714976, 1077996, 1682806, 2502645, 3804460, 5674305, 8340535, 12245241, 18851899, 27570366, 40385431, 59314572
Offset: 2
a(6) = 10: [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1], [3,3], [1,1,4], [1,4,1], [4,1,1].
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 2) -b(n$2, 0, 1):
seq(a(n), n=2..45);
A243120
Number of compositions of n in which the maximal multiplicity of parts equals 3.
Original entry on oeis.org
1, 0, 4, 5, 18, 34, 59, 132, 272, 519, 966, 1746, 3487, 5986, 10570, 19701, 34444, 59250, 101155, 180588, 302788, 515205, 841042, 1449392, 2420163, 3959442, 6472636, 10656987, 17332640, 28234296, 45337971, 72306544, 117761744, 185704091, 295918788, 466574348
Offset: 3
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 3) -b(n$2, 0, 2):
seq(a(n), n=3..50);
A243121
Number of compositions of n in which the maximal multiplicity of parts equals 4.
Original entry on oeis.org
1, 0, 5, 5, 21, 40, 100, 210, 396, 870, 1790, 3510, 6681, 13100, 25320, 47835, 87126, 166195, 299375, 542595, 991036, 1775935, 3145270, 5487805, 9852046, 17092310, 29561070, 50696690, 88015196, 150446590, 256066280, 428469220, 727919426, 1224816005, 2043828145
Offset: 4
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 4) -b(n$2, 0, 3):
seq(a(n), n=4..50);
A243122
Number of compositions of n in which the maximal multiplicity of parts equals 5.
Original entry on oeis.org
1, 0, 6, 6, 27, 49, 131, 279, 635, 1370, 2722, 5877, 12170, 24113, 47660, 94470, 186623, 355400, 680074, 1296600, 2456115, 4535638, 8495447, 15570655, 28505689, 52054671, 94229227, 169184891, 301060621, 540575365, 956101463, 1682865787, 2936425870, 5167830927
Offset: 5
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 5) -b(n$2, 0, 4):
seq(a(n), n=5..50);
A243123
Number of compositions of n in which the maximal multiplicity of parts equals 6.
Original entry on oeis.org
1, 0, 7, 7, 35, 63, 176, 378, 889, 1946, 4298, 9282, 18999, 40565, 84371, 169372, 340683, 684957, 1359758, 2650942, 5142116, 10008642, 19123713, 36370362, 68799767, 129920385, 241668105, 450604609, 830903577, 1529103100, 2800280316, 5100363926, 9233845628
Offset: 6
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 6) -b(n$2, 0, 5):
seq(a(n), n=6..50);
A243124
Number of compositions of n in which the maximal multiplicity of parts equals 7.
Original entry on oeis.org
1, 0, 8, 8, 44, 80, 236, 513, 1246, 2780, 6280, 13786, 30070, 64696, 134585, 285384, 594786, 1207084, 2453682, 4972098, 9946044, 19646041, 38691878, 75939596, 147425468, 283809162, 546291230, 1042095956, 1977521091, 3730060870, 7022446786, 13104269980
Offset: 7
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 7) -b(n$2, 0, 6):
seq(a(n), n=7..50);
A243125
Number of compositions of n in which the maximal multiplicity of parts equals 8.
Original entry on oeis.org
1, 0, 9, 9, 54, 99, 309, 684, 1720, 3918, 9081, 20343, 45261, 99063, 214719, 460428, 965980, 2040096, 4255851, 8706522, 17810088, 36275538, 73017027, 145692324, 289702678, 573412764, 1124242476, 2191850439, 4259718588, 8229423030, 15785908575, 30199934205
Offset: 8
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 8) -b(n$2, 0, 7):
seq(a(n), n=8..50);
A243126
Number of compositions of n in which the maximal multiplicity of parts equals 9.
Original entry on oeis.org
1, 0, 10, 10, 65, 120, 395, 890, 2320, 5401, 12857, 29435, 66955, 149455, 330042, 719882, 1554760, 3326365, 7009606, 14772370, 30835912, 63443345, 130298990, 266321547, 538824877, 1082905293, 2168501310, 4319287751, 8538816117, 16795672263, 32926171923
Offset: 9
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 9) -b(n$2, 0, 8):
seq(a(n), n=9..50);
A243127
Number of compositions of n in which the maximal multiplicity of parts equals 10.
Original entry on oeis.org
1, 0, 11, 11, 77, 143, 495, 1133, 3058, 7271, 17777, 41591, 96767, 220473, 496661, 1103619, 2425929, 5276623, 11370986, 24294028, 51316156, 108047687, 225688551, 466237332, 960231624, 1967794950, 3997987950, 8077762209, 16258984885, 32550495175, 64759902032
Offset: 10
-
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 10) -b(n$2, 0, 9):
seq(a(n), n=10..50);
Comments