|
%I #8 May 10 2018 03:20:45
%S 1,2,3,5,7,11,15,21,29,40,53,72,93,123,159,206,262,336,423,535,669,
%T 837,1037,1288,1584,1950,2385,2915,3542,4305,5202,6284,7558,9082,
%U 10871,13004,15498,18454,21909,25982,30727,36306,42785,50371,59170
%N Number of partitions of n into parts not of the form 21k, 21k+8 or 21k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 9 are greater than 1.
%C Case k=10,i=8 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(2*Pi*sqrt(n/7)) * cos(5*Pi/42) / (sqrt(3) * 7^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 8-21))*(1 - x^(21*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier Gérard_
|
