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%I #8 May 10 2018 03:07:34
%S 1,2,3,5,7,10,14,20,27,37,48,65,84,110,141,182,230,293,367,462,574,
%T 715,881,1089,1333,1633,1987,2419,2926,3540,4259,5124,6136,7344,8754,
%U 10430,12381,14686,17367,20520,24175,28459,33415,39200,45881,53649
%N Number of partitions of n into parts not of the form 17k, 17k+6 or 17k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 7 are greater than 1.
%C Case k=8,i=6 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) * cos(5*Pi/34) / (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+ 6-17))*(1 - x^(17*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier Gérard_