A035996 - OEIS

A035996

Number of partitions of n into parts not of the form 23k, 23k+8 or 23k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 10 are greater than 1.

%I #8 May 10 2018 03:28:30

%S 1,2,3,5,7,11,15,21,29,40,53,72,94,124,160,208,265,340,429,543,680,

%T 852,1057,1314,1619,1995,2443,2990,3638,4426,5356,6477,7800,9384,

%U 11246,13467,16070,19156,22769,27032,32006,37857,44665,52640,61904

%N Number of partitions of n into parts not of the form 23k, 23k+8 or 23k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 10 are greater than 1.

%C Case k=11,i=8 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) * cos(7*Pi/46) / (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+ 8-23))*(1 - x^(23*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,2

%A _Olivier Gérard_