%I
%S 1,0,8,24,80,192,512,1152,2816,6144,14336,30720,69632,
%T 147456,327680,688128,1507328,3145728,6815744,14155776,
%U 30408704,62914560,134217728,276824064,587202560,1207959552,2550136832
%N a(n)=(5(1)^n6*n)*2^(n2)
%C This sequence belongs to a family of sequences with GF(x) = (1+(k+2)*x+(2*k4)*x^2)/(12*x(k+8)*x^2(2*k)*x^3). Among the members of this family are several red king sequences, see A179597. For the sequence given above, which is not a red king sequence, k = 4.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, 8).
%F GF(x) = (12*x12*x^2)/(12*x4*x^2+8*x^3)
%F a(n) = 2*a(n1)+4*a(n2)8*a(n3) with a(1)=1, a(2)=0 and a(3)=8.
%F a(n) = (5(1)^n6*n)*2^(n2)
%t Table[(5(1)^n6n)2^(n2),{n,0,30}] (* or *) LinearRecurrence[{2,4,8},{1,0,8},30] (* _Harvey P. Dale_, Mar 25 2021 *)
%K easy,sign
%O 0,3
%A _Johannes W. Meijer_, Jul 28 2010
