A035398 Number of partitions of n into parts 7k+1 or 7k+4.

1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 5, 7, 7, 7, 9, 12, 12, 13, 16, 19, 19, 22, 26, 30, 31, 36, 41, 45, 48, 56, 62, 68, 75, 85, 92, 101, 112, 125, 134, 149, 165, 180, 193, 216, 237, 256, 277, 309, 335, 360, 392, 434, 466, 503, 550, 602, 643, 697, 760, 824, 881, 958, 1039

Offset

1,4

Links

Table of n, a(n) for n=1..63.

Formula

a(n) ~ exp(2*Pi*sqrt(n/21)) * Gamma(1/7) * Gamma(4/7) / (4 * 3^(3/28) * 7^(11/28) * Pi^(9/7) * n^(17/28)). - Vaclav Kotesovec, Aug 27 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(7k+1))*(1 - x^(7k+4))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Sequence in context: A032544 A200675 A029079 * A104409 A274144 A214628

Adjacent sequences: A035395 A035396 A035397 * A035399 A035400 A035401

Keyword

nonn

Author

Olivier Gérard

Status

approved