cp's OEIS Frontend

A035954 Number of partitions of n into parts not of the form 13k, 13k+6 or 13k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 5 are greater than 1.

%I A035954 #14 May 11 2018 04:22:28
%S A035954 1,1,2,3,5,7,10,13,19,25,34,44,59,75,98,124,159,199,252,312,391,481,
%T A035954 595,727,893,1084,1320,1594,1928,2315,2784,3325,3977,4730,5627,6664,
%U A035954 7894,9310,10981,12905,15162,17756,20787,24263,28310,32946,38317,44462
%N A035954 Number of partitions of n into parts not of the form 13k, 13k+6 or 13k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 5 are greater than 1.
%C A035954 Case k=6,i=6 of Gordon Theorem.
%D A035954 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%H A035954 Seiichi Manyama, <a href="/A035954/b035954.txt">Table of n, a(n) for n = 0..1000</a>
%F A035954 a(n) ~ sin(6*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 A035954 nmax = 60; 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-5)) * (1 - x^(13*k-8)) * (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 A035954 nonn,easy
%O A035954 0,3
%A A035954 _Olivier Gérard_
%E A035954 a(0)=1 prepended by _Seiichi Manyama_, May 08 2018