A035430 Number of partitions of n into parts 7k+1 or 7k+6.

1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7, 8, 8, 9, 10, 12, 14, 16, 17, 19, 20, 23, 26, 30, 33, 37, 39, 43, 47, 53, 59, 66, 71, 77, 83, 92, 101, 113, 123, 134, 144, 156, 169, 187, 204, 223, 240, 259, 278, 303, 329, 360, 389, 420, 449, 485, 522, 567, 613, 663, 710, 763

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Comments

Convolution of A109708 and A109703. - Vaclav Kotesovec, Jan 21 2017

Links

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

Crossrefs

Cf. A284151.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1/((1 - x^(7k+1))*(1 - x^(7k+6))), {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) * sin(Pi/7) * n^(3/4)) * (1 - (3*sqrt(21)/(16*Pi) + 13*Pi/(84*sqrt(21))) / sqrt(n)). - Vaclav Kotesovec, Aug 26 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284151(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 21 2017

Extensions

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