A036011 Number of partitions of n into parts not of the form 25k, 25k+12 or 25k-12. Also number of partitions with at most 11 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 132, 171, 223, 285, 367, 464, 590, 740, 930, 1157, 1442, 1780, 2200, 2699, 3311, 4037, 4922, 5967, 7232, 8724, 10516, 12626, 15147, 18104, 21621, 25739, 30610, 36300, 43005, 50815, 59984, 70642

Offset

0,3

Comments

Case k=12,i=12 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(11*n/3)/5) * 11^(1/4) * cos(Pi/50) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+12-25))*(1 - x^(25*k-12))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A347577 A238869 A326333 * A325856 A104501 A328546

Adjacent sequences: A036008 A036009 A036010 * A036012 A036013 A036014

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

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

Status

approved