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%I #8 May 10 2018 03:04:42
%S 1,1,2,3,4,6,8,11,15,20,26,35,45,58,74,95,119,151,188,235,292,361,443,
%T 546,666,812,986,1196,1442,1740,2088,2504,2993,3572,4248,5051,5983,
%U 7080,8358,9855,11589,13618,15962,18691,21844,25499,29708,34583,40181
%N Number of partitions of n into parts not of the form 17k, 17k+2 or 17k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 7 are greater than 1.
%C Case k=8,i=2 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(2*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+ 2-17))*(1 - x^(17*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,3
%A _Olivier Gérard_