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%I #8 May 10 2018 03:35:06
%S 1,2,3,5,7,11,14,21,28,39,51,70,90,120,154,201,255,328,412,524,654,
%T 821,1017,1267,1558,1924,2353,2884,3507,4272,5166,6256,7531,9069,
%U 10868,13027,15543,18546,22045,26194,31020,36719,43331,51109,60120
%N Number of partitions of n into parts not of the form 25k, 25k+7 or 25k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C Case k=12,i=7 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * cos(11*Pi/50) / (3^(1/4) * 5^(3/2) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 7-25))*(1 - x^(25*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier Gérard_
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