A035946 - OEIS

A035946

Number of partitions in parts not of the form 11k, 11k+3 or 11k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 4 are greater than 1.

%I #8 Nov 21 2015 14:13:48

%S 1,2,2,4,5,8,10,14,18,25,31,42,52,68,84,108,133,168,205,256,311,384,

%T 463,567,681,826,988,1190,1416,1696,2009,2392,2823,3344,3931,4636,

%U 5431,6376,7445,8708,10135,11812,13706,15920,18423,21332,24618,28424

%N Number of partitions in parts not of the form 11k, 11k+3 or 11k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 4 are greater than 1.

%C Case k=5,i=3 of Gordon Theorem.

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

%F a(n) ~ cos(5*Pi/22) * sqrt(2) * 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-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (1 - x^(11*k-9)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 21 2015 *)

%K nonn,easy

%O 1,2

%A _Olivier Gérard_