A035436 Number of partitions of n into parts 7k+3 or 7k+5.

0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 1, 4, 2, 3, 4, 3, 6, 4, 6, 6, 7, 9, 7, 11, 9, 12, 15, 12, 17, 16, 20, 21, 23, 26, 25, 33, 32, 36, 40, 41, 49, 49, 57, 58, 66, 72, 75, 87, 86, 100, 106, 113, 126, 130, 148, 151, 172, 180, 191, 216, 219, 248, 258, 280, 304, 318, 355, 364

Offset

1,10

Links

Table of n, a(n) for n=1..71.

Formula

a(n) ~ exp(2*Pi*sqrt(n/21)) * Gamma(3/7) * Gamma(5/7) / (4 * 3^(9/28) * 7^(5/28) * Pi^(6/7) * n^(23/28)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(7k+3))*(1 - x^(7k+5))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)

Crossrefs

Sequence in context: A106190 A029290 A115311 * A242210 A035369 A129719

Adjacent sequences: A035433 A035434 A035435 * A035437 A035438 A035439

Keyword

nonn

Author

Olivier Gérard

Status

approved