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%I #8 May 10 2018 03:23:41
%S 0,1,1,2,2,4,4,7,8,12,14,21,24,34,41,55,66,88,105,137,165,209,252,318,
%T 381,474,569,700,837,1024,1219,1480,1760,2120,2514,3015,3561,4248,
%U 5008,5944,6986,8261,9680,11402,13331,15641,18240,21338,24817,28941
%N Number of partitions in parts not of the form 23k, 23k+1 or 23k-1. Also number of partitions with no part of size 1 and differences between parts at distance 10 are greater than 1.
%C Case k=11,i=1 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * sin(Pi/23) / (3^(1/4) * 23^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 1-23))*(1 - x^(23*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,4
%A _Olivier Gérard_
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