A035450 Number of partitions of n into parts 8k+1 or 8k+4.

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 6, 7, 7, 7, 9, 11, 12, 12, 15, 18, 19, 19, 23, 27, 29, 30, 35, 41, 44, 45, 51, 59, 64, 66, 75, 86, 93, 96, 107, 121, 131, 136, 150, 170, 184, 191, 209, 234, 253, 264, 287, 320, 347, 362, 391, 433, 468, 489, 527, 581, 628, 658, 705, 773

Offset

1,4

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

G.f.: Product 1/((1-x^(8k+1))*(1-x^(8k+4))); k=1..inf.

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(1/8) / (8 * 2^(5/16) * 3^(1/16) * Pi^(7/8) * n^(9/16)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+4))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 1}~Join~{Range[0, kmax]*8 + 4}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Sequence in context: A124789 A103372 A029082 * A234537 A029126 A269850

Adjacent sequences: A035447 A035448 A035449 * A035451 A035452 A035453

Keyword

nonn

Author

Olivier Gérard

Status

approved