A035978 - OEIS

%I #14 May 09 2018 08:52:00

%S 1,1,2,3,5,7,11,15,22,29,40,53,72,93,123,158,205,260,333,418,529,659,

%T 824,1019,1264,1551,1908,2328,2843,3448,4185,5048,6092,7313,8777,

%U 10489,12531,14910,17733,21019,24896,29399,34692,40824,48004,56307

%N Number of partitions of n into parts not of the form 19k, 19k+9 or 19k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 8 are greater than 1.

%C Case k=9,i=9 of Gordon Theorem.

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

%H Seiichi Manyama, <a href="/A035978/b035978.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 09 2018

%t nmax = 50; CoefficientList[Series[Product[((1 - x^(19*k))*(1 - x^(19*k - 9))*(1 - x^(19*k - 10)))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 09 2018 *)

%K nonn,easy

%O 0,3

%A _Olivier Gérard_

%E a(0)=1 prepended by _Seiichi Manyama_, May 08 2018