A035435 Number of partitions of n into parts 7k+3 or 7k+4.

1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 4, 6, 7, 7, 7, 10, 10, 10, 12, 15, 14, 16, 19, 21, 21, 25, 28, 30, 31, 37, 40, 42, 46, 54, 55, 60, 68, 74, 76, 87, 95, 101, 108, 122, 130, 139, 151, 168, 176, 190, 209, 227, 237, 261, 284, 302, 321, 355, 378, 402, 434

Offset

0,11

Comments

Convolution of A109706 and A109705. - Vaclav Kotesovec, Jan 21 2017

Links

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

Formula

a(n) ~ exp(2*Pi*sqrt(n/21)) / (4 * 21^(1/4) * cos(Pi/14) * n^(3/4)) * (1 + (23*Pi/(84*sqrt(21)) - 3*sqrt(21)/(16*Pi)) / sqrt(n)). - Vaclav Kotesovec, Aug 26 2015, extended Jan 24 2017

Mathematica

nmax = 100; CoefficientList[Series[Product[1/((1 - x^(7k+3))*(1 - x^(7k+4))), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 26 2015 *)

Crossrefs

Sequence in context: A123577 A005854 A169991 * A169992 A025775 A169993

Adjacent sequences: A035432 A035433 A035434 * A035436 A035437 A035438

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved