A035969 - OEIS

A035969

Number of partitions of n into parts not of the form 17k, 17k+8 or 17k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 7 are greater than 1.

%I #13 May 10 2018 03:09:32

%S 1,1,2,3,5,7,11,15,21,28,39,51,69,89,117,150,194,245,313,392,494,614,

%T 766,944,1168,1430,1754,2135,2601,3146,3810,4585,5519,6611,7917,9440,

%U 11253,13361,15856,18755,22169,26124,30766,36132,42401,49639,58063

%N Number of partitions of n into parts not of the form 17k, 17k+8 or 17k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 7 are greater than 1.

%C Case k=8,i=8 of Gordon Theorem.

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

%H Seiichi Manyama, <a href="/A035969/b035969.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * cos(Pi/34) / (3^(1/4) * 17^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018

%t nmax = 60; CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 8-17))*(1 - x^(17*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 0,3

%A _Olivier Gérard_

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