cp's OEIS Frontend

A035949 Number of partitions in parts not of the form 13k, 13k+1 or 13k-1. Also number of partitions with no part of size 1 and differences between parts at distance 5 are greater than 1.

%I A035949 #8 Nov 22 2015 12:34:52
%S A035949 0,1,1,2,2,4,4,7,8,12,14,20,23,32,39,51,61,80,95,122,146,183,219,273,
%T A035949 324,399,475,578,685,830,979,1177,1387,1655,1945,2311,2705,3198,3737,
%U A035949 4396,5121,6003,6973,8143,9439,10981,12697,14730,16987,19648,22614
%N A035949 Number of partitions in parts not of the form 13k, 13k+1 or 13k-1. Also number of partitions with no part of size 1 and differences between parts at distance 5 are greater than 1.
%C A035949 Case k=6,i=1 of Gordon Theorem.
%D A035949 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F A035949 a(n) ~ sin(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 A035949 nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 22 2015 *)
%K A035949 nonn,easy
%O A035949 1,4
%A A035949 _Olivier Gérard_