A035999 Number of partitions of n into parts not of the form 23k, 23k+11 or 23k-11. Also number of partitions with at most 10 parts of size 1 and differences between parts at distance 10 are greater than 1.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 98, 130, 168, 219, 279, 359, 453, 575, 720, 904, 1122, 1397, 1722, 2125, 2603, 3190, 3883, 4729, 5725, 6930, 8349, 10053, 12053, 14444, 17243, 20569, 24457, 29055, 34414, 40728, 48070, 56683, 66682

Offset

0,3

Comments

Case k=11, i=11 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Andrews-Gordon Identity

Formula

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * cos(Pi/46) / (3^(1/4) * 23^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+11-23))*(1 - x^(23*k-11))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A008633 A347576 A238868 * A036010 A328545 A192061

Adjacent sequences: A035996 A035997 A035998 * A036000 A036001 A036002

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Seiichi Manyama, May 10 2018

Status

approved