%I #8 May 10 2018 03:33:07
%S 1,2,3,4,6,9,12,17,23,31,41,55,71,93,120,154,196,250,314,396,494,616,
%T 763,945,1161,1427,1744,2128,2585,3138,3790,4575,5502,6606,7908,9455,
%U 11268,13415,15928,18886,22341,26397,31116,36638,43053,50527,59192
%N Number of partitions of n into parts not of the form 25k, 25k+4 or 25k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C Case k=12,i=4 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) * sin(4*Pi/25) / (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+ 4-25))*(1 - x^(25*k- 4))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier Gérard_