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%I #8 May 10 2018 03:21:22
%S 1,2,3,5,7,11,15,22,29,41,54,73,95,126,162,211,268,344,433,549,685,
%T 859,1064,1322,1626,2004,2449,2997,3641,4427,5350,6467,7776,9350,
%U 11192,13392,15961,19014,22572,26779,31671,37430,44114,51950,61026
%N Number of partitions of n into parts not of the form 21k, 21k+9 or 21k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 9 are greater than 1.
%C Case k=10,i=9 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)) * cos(Pi/14) / (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+ 9-21))*(1 - x^(21*k- 9))/(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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