A035991 - OEIS

A035991

Number of partitions in parts not of the form 23k, 23k+3 or 23k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 10 are greater than 1.

%I #8 May 10 2018 03:25:03

%S 1,2,2,4,5,8,10,15,19,27,34,47,59,79,99,130,162,209,259,329,406,510,

%T 625,778,949,1170,1420,1738,2100,2553,3070,3710,4443,5340,6369,7618,

%U 9052,10777,12760,15130,17853,21088,24803,29193,34233,40158,46954

%N Number of partitions in parts not of the form 23k, 23k+3 or 23k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 10 are greater than 1.

%C Case k=11,i=3 of Gordon Theorem.

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

%F a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * sin(3*Pi/23) / (3^(1/4) * 23^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018

%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 3-23))*(1 - x^(23*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,2

%A _Olivier Gérard_