A035951 - OEIS

%I #8 Nov 22 2015 12:35:10

%S 1,2,2,4,5,8,10,15,19,26,33,45,56,74,92,119,147,187,230,289,353,438,

%T 532,655,791,965,1160,1405,1681,2023,2409,2883,3420,4070,4809,5698,

%U 6707,7911,9281,10904,12750,14925,17397,20296,23590,27431,31795,36864

%N Number of partitions in parts not of the form 13k, 13k+3 or 13k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 5 are greater than 1.

%C Case k=6,i=3 of Gordon Theorem.

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

%F a(n) ~ sin(3*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; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-2)) * (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-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 22 2015 *)

%K nonn,easy

%O 1,2

%A _Olivier Gérard_