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%I #8 May 10 2018 02:58:04
%S 0,1,1,2,2,4,4,7,8,12,14,21,24,33,40,53,64,84,100,129,155,195,234,293,
%T 349,431,515,629,748,909,1076,1298,1535,1837,2166,2582,3032,3595,4214,
%U 4972,5810,6831,7959,9321,10837,12643,14662,17057,19728,22880,26409
%N Number of partitions in parts not of the form 15k, 15k+1 or 15k-1. Also number of partitions with no part of size 1 and differences between parts at distance 6 are greater than 1.
%C Case k=7,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(2*n/15)) * 2^(1/4) * sin(Pi/15) / (15^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 1-15))*(1 - x^(15*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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