%I #8 Jun 13 2015 00:55:27
%S 1,5,20,58,136,282,532,931,1540,2432,3692,5427,7760,10829,14800,19858,
%T 26207,34085,43752,55491,69624,86499,106491,130019,157532,189509,
%U 226479,269005,317683,373165,436140,507334,587535,677571,778311,890691,1015691,1154336
%N Number of partitions of 4n into at most 6 parts.
%H Colin Barker, <a href="/A256540/b256540.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
%F G.f.: (3*x^8+5*x^7+11*x^6+11*x^5+13*x^4+10*x^3+8*x^2+2*x+1) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).
%F a(n) = A001402(4n). - _Alois P. Heinz_, Apr 01 2015
%e For n=1 the 5 partitions of 1*4 = 4 are [4], [1,3], [2,2], [1,1,2] and [1,1,1,1].
%o (PARI) concat(1, vector(40, n, k=0; forpart(p=4*n, k++, , [1,6]); k))
%o (PARI) Vec((3*x^8+5*x^7+11*x^6+11*x^5+13*x^4+10*x^3+8*x^2+2*x+1) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100))
%Y Cf. A001402, A238340 (4 parts), A256539 (5 parts).
%K nonn,easy
%O 0,2
%A _Colin Barker_, Apr 01 2015