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A035994 Number of partitions of n into parts not of the form 23k, 23k+6 or 23k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 10 are greater than 1. 0

%I

%S 1,2,3,5,7,10,14,20,27,37,49,66,86,113,146,189,240,307,387,489,611,

%T 764,947,1175,1446,1779,2176,2660,3233,3928,4749,5737,6902,8295,9934,

%U 11884,14170,16877,20045,23780,28136,33254,39210,46180,54273,63711

%N Number of partitions of n into parts not of the form 23k, 23k+6 or 23k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 10 are greater than 1.

%C Case k=11,i=6 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(11*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+ 6-23))*(1 - x^(23*k- 6))/(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 August 10 03:08 EDT 2020. Contains 336367 sequences. (Running on oeis4.)