A035433 Number of partitions of n into parts 7k+2 or 7k+5.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 4, 3, 5, 4, 6, 6, 7, 8, 8, 10, 11, 12, 14, 14, 18, 17, 22, 21, 26, 27, 30, 34, 36, 41, 44, 48, 54, 56, 66, 66, 78, 80, 91, 97, 106, 116, 124, 137, 147, 159, 175, 184, 207, 215, 241, 252, 279, 297, 321, 348, 371, 404, 432, 464, 503

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Comments

Convolution of A109707 and A109704. - Vaclav Kotesovec, Jan 21 2017

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1/((1 - x^(7k+2))*(1 - x^(7k+5))), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 26 2015 *)

Formula

a(n) ~ exp(2*Pi*sqrt(n/21)) / (4 * 21^(1/4) * cos(3*Pi/14) * n^(3/4)) * (1 + (11*Pi/(84*sqrt(21)) - 3*sqrt(21)/(16*Pi)) / sqrt(n)). - Vaclav Kotesovec, Aug 26 2015, extended Jan 24 2017

Extensions

Prepended a(0)=1 from Vaclav Kotesovec, Jan 23 2017