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%I #4 Mar 25 2021 19:10:46
%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)^n-6*n)*2^(n-2)
%C This sequence belongs to a family of sequences with GF(x) = (1+(k+2)*x+(2*k-4)*x^2)/(1-2*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) = (1-2*x-12*x^2)/(1-2*x-4*x^2+8*x^3)
%F a(n) = 2*a(n-1)+4*a(n-2)-8*a(n-3) with a(1)=1, a(2)=0 and a(3)=-8.
%F a(n) = (5-(-1)^n-6*n)*2^(n-2)
%t Table[(5-(-1)^n-6n)2^(n-2),{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
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