cp's OEIS Frontend

A035952 Number of partitions of n into parts not of the form 13k, 13k+4 or 13k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 5 are greater than 1.

%I A035952 #8 Nov 22 2015 12:35:16
%S A035952 1,2,3,4,6,9,12,17,22,30,39,52,66,86,109,139,174,220,272,340,419,517,
%T A035952 632,775,940,1144,1381,1668,2002,2406,2873,3433,4082,4852,5745,6801,
%U A035952 8018,9452,11105,13039,15266,17864,20845,24310,28284,32881,38145
%N A035952 Number of partitions of n into parts not of the form 13k, 13k+4 or 13k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 5 are greater than 1.
%C A035952 Case k=6,i=4 of Gordon Theorem.
%D A035952 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F A035952 a(n) ~ sin(4*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 A035952 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-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (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 A035952 nonn,easy
%O A035952 1,2
%A A035952 _Olivier Gérard_