A035998 - OEIS

A035998

Number of partitions of n into parts not of the form 23k, 23k+10 or 23k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 10 are greater than 1.

%I #8 May 10 2018 03:29:55

%S 1,2,3,5,7,11,15,22,30,41,55,75,97,129,167,217,277,356,449,570,714,

%T 895,1112,1384,1705,2104,2578,3157,3844,4680,5665,6857,8261,9943,

%U 11923,14286,17052,20339,24184,28724,34023,40260,47515,56024,65904

%N Number of partitions of n into parts not of the form 23k, 23k+10 or 23k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 10 are greater than 1.

%C Case k=11,i=10 of Gordon Theorem.

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

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

%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+10-23))*(1 - x^(23*k-10))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,2

%A _Olivier Gérard_