Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 May 09 2018 11:14:08
%S 0,0,1,1,1,1,2,3,3,3,5,7,7,8,12,15,16,19,25,31,35,40,50,62,69,80,99,
%T 117,133,154,184,217,247,283,335,391,443,507,593,685,776,886,1024,
%U 1175,1331,1510,1733,1980,2232,2526,2883,3271,3682,4154,4710,5324
%N Number of partitions of n into parts not of form 4k+2, 24k, 24k+1 or 24k-1. Also number of partitions in which no odd part is repeated, with no part 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=1 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 - 23))*(1 - x^(24*k - 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 09 2018 *)
%K nonn,easy
%O 1,7
%A _Olivier Gérard_