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A035995 Number of partitions of n into parts not of the form 23k, 23k+7 or 23k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 10 are greater than 1. 0

%I

%S 1,2,3,5,7,11,14,21,28,39,51,70,90,120,154,200,254,327,410,521,650,

%T 815,1009,1256,1543,1904,2327,2849,3462,4214,5091,6160,7410,8915,

%U 10675,12785,15242,18172,21583,25623,30320,35862,42285,49835,58576

%N Number of partitions of n into parts not of the form 23k, 23k+7 or 23k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 10 are greater than 1.

%C Case k=11,i=7 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(9*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+ 7-23))*(1 - x^(23*k- 7))/(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 19 12:03 EDT 2020. Contains 337178 sequences. (Running on oeis4.)