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%I #8 May 10 2018 02:59:52
%S 1,2,2,4,5,8,10,15,19,27,34,46,58,77,96,125,155,198,244,308,378,471,
%T 574,709,860,1053,1270,1544,1854,2239,2676,3213,3824,4567,5414,6435,
%U 7600,8993,10584,12474,14632,17180,20088,23505,27403,31960,37154
%N Number of partitions in parts not of the form 15k, 15k+3 or 15k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 6 are greater than 1.
%C Case k=7,i=3 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)) * sqrt(5 - sqrt(5)) / (2^(5/4) * 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+ 3-15))*(1 - x^(15*k- 3))/(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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