cp's OEIS Frontend

A035953 Number of partitions of n into parts not of the form 13k, 13k+5 or 13k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 5 are greater than 1.

%I A035953 #8 Nov 22 2015 12:35:24
%S A035953 1,2,3,5,6,10,13,18,24,33,42,57,72,94,119,153,190,242,299,374,460,570,
%T A035953 695,855,1036,1262,1523,1843,2210,2660,3175,3797,4514,5372,6357,7533,
%U A035953 8880,10474,12306,14459,16925,19818,23125,26981,31392,36512,42355
%N A035953 Number of partitions of n into parts not of the form 13k, 13k+5 or 13k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 5 are greater than 1.
%C A035953 Case k=6,i=5 of Gordon Theorem.
%D A035953 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F A035953 a(n) ~ sin(5*Pi/13) * 5^(1/4) * exp(2*Pi*sqrt(5*n/39)) / (3^(1/4) * 13^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Nov 22 2015
%t A035953 nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 22 2015 *)
%K A035953 nonn,easy
%O A035953 1,2
%A A035953 _Olivier Gérard_