A035397 Number of partitions of n into parts 7k+1 or 7k+3.

1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 19, 21, 24, 27, 30, 34, 39, 44, 49, 55, 61, 67, 76, 84, 94, 105, 116, 128, 141, 155, 171, 189, 209, 229, 252, 275, 301, 330, 361, 395, 433, 472, 514, 560, 609, 662, 722, 784, 852, 924, 1001, 1084, 1175, 1272

Offset

1,3

Links

Table of n, a(n) for n=1..61.

Formula

a(n) ~ exp(2*Pi*sqrt(n/21)) * Gamma(1/7) * Gamma(3/7) / (4 * 3^(1/28) * 7^(13/28) * Pi^(10/7) * n^(15/28)). - Vaclav Kotesovec, Aug 27 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(7k+1))*(1 - x^(7k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Sequence in context: A036847 A282379 A029055 * A033295 A018049 A238210

Adjacent sequences: A035394 A035395 A035396 * A035398 A035399 A035400

Keyword

nonn

Author

Olivier Gérard

Status

approved