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%I #8 May 10 2018 03:37:15
%S 1,2,3,5,7,11,15,22,30,42,55,76,99,131,170,222,283,365,461,586,735,
%T 924,1148,1432,1767,2183,2678,3286,4004,4883,5918,7172,8651,10428,
%U 12516,15017,17946,21430,25509,30337,35969,42614,50347,59428,69982
%N Number of partitions of n into parts not of the form 25k, 25k+11 or 25k-11. Also number of partitions with at most 10 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C Case k=12,i=11 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(3*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+11-25))*(1 - x^(25*k-11))/(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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