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%I #8 May 10 2018 03:00:40
%S 1,2,3,4,6,9,12,17,23,31,40,54,69,90,115,147,185,235,292,366,453,561,
%T 689,848,1033,1261,1529,1853,2233,2693,3227,3869,4618,5507,6543,7771,
%U 9194,10872,12817,15096,17732,20814,24365,28501,33265,38786,45133
%N Number of partitions of n into parts not of the form 15k, 15k+4 or 15k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 6 are greater than 1.
%C Case k=7,i=4 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) * cos(7*Pi/30) / (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+ 4-15))*(1 - x^(15*k- 4))/(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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