A035964 - OEIS

A035964

Number of partitions in parts not of the form 17k, 17k+3 or 17k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 7 are greater than 1.

%I #8 May 10 2018 03:05:25

%S 1,2,2,4,5,8,10,15,19,27,34,47,59,78,98,128,159,204,252,319,392,490,

%T 599,742,902,1107,1339,1632,1964,2378,2849,3429,4091,4897,5819,6933,

%U 8207,9733,11481,13562,15943,18761,21985,25780,30121,35204,41013

%N Number of partitions in parts not of the form 17k, 17k+3 or 17k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 7 are greater than 1.

%C Case k=8,i=3 of Gordon Theorem.

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

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

%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 3-17))*(1 - x^(17*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,2

%A _Olivier Gérard_