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%I #8 May 10 2018 03:08:39
%S 1,2,3,5,7,11,14,21,28,38,50,68,87,115,147,190,240,307,383,484,601,
%T 749,923,1143,1397,1715,2086,2541,3073,3722,4476,5390,6454,7728,9212,
%U 10983,13035,15471,18295,21624,25478,30005,35229,41344,48393,56602
%N Number of partitions of n into parts not of the form 17k, 17k+7 or 17k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 7 are greater than 1.
%C Case k=8,i=7 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(3*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+ 7-17))*(1 - x^(17*k- 7))/(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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