A036029 - 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_