%I #8 May 10 2018 03:34:26
%S 1,2,3,5,7,10,14,20,27,37,49,66,86,113,146,189,241,308,388,491,614,
%T 768,953,1183,1457,1794,2196,2686,3268,3973,4807,5812,6998,8416,10087,
%U 12076,14411,17177,20417,24239,28703,33949,40060,47217,55535,65240
%N Number of partitions of n into parts not of the form 25k, 25k+6 or 25k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C Case k=12,i=6 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(6*Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 6-25))*(1 - x^(25*k- 6))/(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_