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%I #8 May 10 2018 03:35:52
%S 1,2,3,5,7,11,15,21,29,40,53,72,94,124,161,209,266,342,432,547,686,
%T 860,1068,1329,1639,2021,2478,3035,3696,4501,5452,6598,7954,9577,
%U 11488,13769,16445,19619,23341,27734,32866,38907,45944,54191,63784
%N Number of partitions of n into parts not of the form 25k, 25k+8 or 25k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C Case k=12,i=8 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(9*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+ 8-25))*(1 - x^(25*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier Gérard_