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A035943 Number of partitions of n into parts not of the form 9k, 9k+4 or 9k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 3 are greater than 1. 2

%I

%S 1,1,2,3,4,5,8,10,14,18,24,30,40,49,63,78,98,120,150,182,224,271,330,

%T 396,480,572,687,817,974,1151,1367,1608,1898,2226,2614,3053,3573,4157,

%U 4844,5620,6524,7544,8731,10066,11611,13353,15356,17612,20203,23112

%N Number of partitions of n into parts not of the form 9k, 9k+4 or 9k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 3 are greater than 1.

%C Case k=4,i=4 of Gordon Theorem.

%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

%H Seiichi Manyama, <a href="/A035943/b035943.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ cos(Pi/18) * exp(2*Pi*sqrt(n)/3) / (3*sqrt(3)*n^(3/4)). - _Vaclav Kotesovec_, Nov 12 2015

%t nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-2)) * (1 - x^(9*k-3)) * (1 - x^(9*k-6)) * (1 - x^(9*k-7)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 12 2015 *)

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_

%E a(0)=1 prepended by _Seiichi Manyama_, May 08 2018

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Last modified December 2 09:48 EST 2020. Contains 338876 sequences. (Running on oeis4.)