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%I #11 May 09 2018 11:29:20
%S 1,1,2,3,4,5,6,9,12,14,18,24,30,36,45,57,69,83,101,124,150,177,212,
%T 257,305,358,425,505,594,694,813,956,1116,1293,1504,1753,2029,2339,
%U 2702,3123,3593,4120,4729,5430,6215,7090,8094,9245,10525,11955,13587
%N Number of partitions of n into parts not of form 4k+2, 24k, 24k+7 or 24k-7. Also number of partitions in which no odd part is repeated, with at most 3 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=4 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 - 17))*(1 - x^(24*k - 7))/(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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