A035954 - OEIS

%I #14 May 11 2018 04:22:28

%S 1,1,2,3,5,7,10,13,19,25,34,44,59,75,98,124,159,199,252,312,391,481,

%T 595,727,893,1084,1320,1594,1928,2315,2784,3325,3977,4730,5627,6664,

%U 7894,9310,10981,12905,15162,17756,20787,24263,28310,32946,38317,44462

%N 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 Case k=6,i=6 of Gordon Theorem.

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

%H Seiichi Manyama, <a href="/A035954/b035954.txt">Table of n, a(n) for n = 0..1000</a>

%F 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 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 nonn,easy

%O 0,3

%A _Olivier Gérard_

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