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%I #8 Nov 22 2015 12:35:02
%S 1,1,2,3,4,6,8,11,15,20,25,34,43,55,70,89,111,140,173,215,265,326,397,
%T 487,590,715,863,1041,1247,1497,1785,2129,2530,3003,3551,4200,4947,
%U 5823,6837,8020,9380,10967,12787,14898,17322,20120,23322,27018,31235
%N Number of partitions of n into parts not of the form 13k, 13k+2 or 13k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 5 are greater than 1.
%C Case k=6,i=2 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ sin(2*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-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-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 22 2015 *)
%K nonn,easy
%O 1,3
%A _Olivier Gérard_
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