A035944 - OEIS

%I #9 Nov 21 2015 13:37:21

%S 0,1,1,2,2,4,4,7,8,11,13,19,22,30,36,47,56,73,86,110,131,163,194,241,

%T 284,348,412,499,588,709,832,996,1168,1387,1622,1919,2235,2631,3060,

%U 3584,4156,4852,5610,6525,7530,8724,10044,11607,13328,15355,17600

%N Number of partitions in parts not of the form 11k, 11k+1 or 11k-1. Also number of partitions with no part of size 1 and differences between parts at distance 4 are greater than 1.

%C Case k=5,i=1 of Gordon Theorem.

%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

%F a(n) ~ sqrt(2) * sin(Pi/11) * exp(4*Pi*sqrt(n/33)) / (3^(1/4) * 11^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Nov 21 2015

%t nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(11*k-2)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-9)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 21 2015 *)

%K nonn,easy

%O 1,4

%A _Olivier Gérard_