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%I #8 May 10 2018 03:03:58
%S 0,1,1,2,2,4,4,7,8,12,14,21,24,34,41,54,65,86,103,133,160,202,243,305,
%T 364,451,540,661,788,960,1139,1377,1632,1958,2314,2764,3253,3866,4542,
%U 5370,6289,7410,8652,10154,11830,13830,16072,18735,21714,25234,29185
%N Number of partitions in parts not of the form 17k, 17k+1 or 17k-1. Also number of partitions with no part of size 1 and differences between parts at distance 7 are greater than 1.
%C Case k=8,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(7*n/51)) * 7^(1/4) * sin(Pi/17) / (3^(1/4) * 17^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 1-17))*(1 - x^(17*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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