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%I #8 May 10 2018 03:19:09
%S 1,2,3,5,6,10,13,19,25,35,45,62,79,105,134,174,219,282,352,446,554,
%T 694,855,1063,1301,1602,1952,2386,2889,3511,4231,5109,6130,7363,8794,
%U 10515,12507,14885,17642,20910,24690,29157,34313,40373,47366,55547
%N Number of partitions of n into parts not of the form 21k, 21k+5 or 21k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 9 are greater than 1.
%C Case k=10,i=5 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(2*Pi*sqrt(n/7)) * sin(5*Pi/21) / (sqrt(3) * 7^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 5-21))*(1 - x^(21*k- 5))/(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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