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%I #8 May 10 2018 03:12:23
%S 1,2,3,4,6,9,12,17,23,31,41,55,71,93,119,153,194,247,309,389,484,602,
%T 743,918,1124,1378,1679,2043,2474,2995,3606,4341,5204,6231,7436,8866,
%U 10534,12506,14804,17504,20645,24325,28589,33569,39332,46032,53771
%N Number of partitions of n into parts not of the form 19k, 19k+4 or 19k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 8 are greater than 1.
%C Case k=9,i=4 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * sin(4*Pi/19) / (3^(1/4) * 19^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 4-19))*(1 - x^(19*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_
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