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%I #8 May 10 2018 03:33:45
%S 1,2,3,5,6,10,13,19,25,35,45,62,79,105,134,175,220,284,355,450,560,
%T 703,867,1080,1324,1633,1993,2441,2960,3604,4350,5262,6324,7610,9104,
%U 10905,12993,15490,18390,21835,25825,30550,36013,42445,49880,58595
%N Number of partitions of n into parts not of the form 25k, 25k+5 or 25k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C Case k=12,i=5 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*(3 - sqrt(5)))/30)^(1/4) / (10 * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 5-25))*(1 - x^(25*k- 5))/(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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