%I #8 May 10 2018 03:13:07
%S 1,2,3,5,6,10,13,19,25,35,45,62,79,104,133,173,217,279,348,440,546,
%T 683,840,1043,1275,1567,1907,2328,2815,3416,4111,4957,5940,7125,8498,
%U 10148,12055,14327,16959,20075,23673,27920,32816,38562,45185,52923
%N Number of partitions of n into parts not of the form 19k, 19k+5 or 19k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 8 are greater than 1.
%C Case k=9,i=5 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(9*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 5-19))*(1 - x^(19*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier GĂ©rard_
|