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%I #12 May 09 2018 12:02:17
%S 1,1,2,3,4,5,7,10,13,16,20,27,33,40,51,64,78,94,115,141,170,202,243,
%T 294,349,411,489,581,683,800,940,1105,1290,1498,1745,2034,2355,2718,
%U 3145,3636,4184,4804,5520,6340,7258,8289,9472,10821,12324,14011,15935
%N Number of partitions of n into parts not of form 4k+2, 24k, 24k+11 or 24k-11. Also number of partitions in which no odd part is repeated, with at most 5 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.
%C Case k=6,i=6 of Gordon/Goellnitz/Andrews Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
%F a(n) ~ 5^(1/4) * sqrt(2 + sqrt(2 + sqrt(3))) * exp(sqrt(5*n/3)*Pi/2) / (8 * 3^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 09 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(24*k))*(1 - x^(24*k - 13))*(1 - x^(24*k - 11))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 09 2018 *)
%K nonn,easy
%O 1,3
%A _Olivier Gérard_
%E Name corrected by _Vaclav Kotesovec_, May 09 2018
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