A036001 - OEIS

A036001

Number of partitions of n into parts not of the form 25k, 25k+2 or 25k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 11 are greater than 1.

%I #8 May 10 2018 03:31:51

%S 1,1,2,3,4,6,8,11,15,20,26,35,45,58,75,96,121,154,193,242,302,375,462,

%T 572,701,858,1047,1275,1545,1872,2257,2718,3264,3912,4674,5581,6641,

%U 7892,9359,11082,13090,15447,18186,21385,25102,29425,34430,40247

%N Number of partitions of n into parts not of the form 25k, 25k+2 or 25k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 11 are greater than 1.

%C Case k=12,i=2 of Gordon Theorem.

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

%F a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(2*Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018

%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 2-25))*(1 - x^(25*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,3

%A _Olivier Gérard_