A035461 Number of partitions of n into parts 8k+3 or 8k+6.

0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 3, 0, 2, 3, 0, 3, 4, 1, 4, 4, 3, 5, 5, 5, 6, 6, 8, 7, 9, 10, 8, 13, 13, 10, 18, 15, 14, 23, 18, 20, 29, 21, 29, 34, 27, 38, 40, 36, 49, 46, 49, 59, 56, 65, 71, 70, 83, 82, 91, 102, 98, 116, 122, 119, 148, 143, 150, 180, 169, 189, 217, 202, 237

Offset

1,6

Links

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

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/8) * Gamma(3/4) / (4 * 2^(9/16) * 3^(5/16) * Pi^(7/8) * n^(13/16)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+3))*(1 - x^(8k+6))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 3}~Join~{Range[0, kmax]*8 + 6}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 04 2020 *)

Crossrefs

Cf. A035692.

Sequence in context: A111775 A325166 A025844 * A118508 A029305 A339441

Adjacent sequences: A035458 A035459 A035460 * A035462 A035463 A035464

Keyword

nonn

Author

Olivier Gérard

Status

approved