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A035997 Number of partitions of n into parts not of the form 23k, 23k+9 or 23k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 10 are greater than 1. 0

%I

%S 1,2,3,5,7,11,15,22,29,41,54,74,96,127,164,214,272,350,441,560,700,

%T 879,1090,1357,1671,2062,2524,3093,3762,4581,5543,6709,8078,9725,

%U 11655,13965,16664,19875,23623,28060,33225,39314,46388,54691,64320

%N Number of partitions of n into parts not of the form 23k, 23k+9 or 23k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 10 are greater than 1.

%C Case k=11,i=9 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(5*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+ 9-23))*(1 - x^(23*k- 9))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,2

%A _Olivier GĂ©rard_

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Last modified September 25 23:23 EDT 2020. Contains 337346 sequences. (Running on oeis4.)