A035442 Number of partitions of n into parts 8k or 8k+2.

0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 3, 0, 3, 0, 5, 0, 7, 0, 8, 0, 8, 0, 11, 0, 15, 0, 17, 0, 18, 0, 23, 0, 30, 0, 35, 0, 37, 0, 45, 0, 57, 0, 66, 0, 71, 0, 84, 0, 104, 0, 121, 0, 131, 0, 151, 0, 183, 0, 212, 0, 231, 0, 263, 0, 313, 0, 362, 0, 396, 0, 446, 0, 523, 0, 601, 0, 660, 0

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

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

Crossrefs

Cf. A035679.

Programs

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+2))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 50; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 2}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Formula

If n is even, a(n) ~ 2 * exp(Pi*sqrt(n/6)) * Gamma(5/4) / (6^(3/8) * Pi^(3/4) * n^(7/8)). - Vaclav Kotesovec, Aug 26 2015