A035441 Number of partitions of n into parts 8k or 8k+1.

1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 5, 7, 8, 8, 8, 8, 8, 8, 11, 15, 17, 18, 18, 18, 18, 18, 23, 30, 35, 37, 38, 38, 38, 38, 45, 57, 66, 71, 73, 74, 74, 74, 85, 104, 121, 131, 136, 138, 139, 139, 154, 184, 212, 231, 241, 246, 248, 249, 271, 316, 363, 396, 416

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

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

Crossrefs

Cf. A035672.

Programs

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+1))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 68; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 1}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 02 2020 *)

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(9/8) * 2^(7/16) / (3^(5/16) * Pi^(7/8) * n^(13/16)). - Vaclav Kotesovec, Aug 26 2015