A035990 - OEIS

A035990

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

%I #8 May 10 2018 03:24:21

%S 1,1,2,3,4,6,8,11,15,20,26,35,45,58,75,96,121,154,193,242,301,374,461,

%T 570,698,854,1042,1268,1535,1859,2240,2696,3235,3875,4627,5521,6565,

%U 7797,9240,10934,12906,15220,17907,21043,24683,28915,33811,39497

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

%C Case k=11,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(10*n/69)) * 10^(1/4) * sin(2*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+ 2-23))*(1 - x^(23*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_