A035429 Number of partitions of n into parts 7k+1 or 7k+5.

1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 23, 26, 28, 32, 35, 39, 44, 48, 54, 58, 65, 72, 79, 87, 95, 105, 115, 126, 138, 150, 165, 180, 197, 213, 233, 254, 276, 300, 325, 354, 383, 415, 451, 487, 528, 569, 618, 666, 718, 776, 836

Offset

1,5

Links

Table of n, a(n) for n=1..64.

Formula

a(n) ~ exp(2*Pi*sqrt(n/21)) * Gamma(1/7) * Gamma(5/7) / (4 * 3^(5/28) * 7^(9/28) * Pi^(8/7) * n^(19/28)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

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

Crossrefs

Sequence in context: A174576 A288122 A060970 * A280169 A018117 A086936

Adjacent sequences: A035426 A035427 A035428 * A035430 A035431 A035432

Keyword

nonn

Author

Olivier Gérard

Status

approved