This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179609 #6 Jun 02 2025 03:01:54
%S A179609 1,0,-8,-24,-80,-192,-512,-1152,-2816,-6144,-14336,-30720,-69632,
%T A179609 -147456,-327680,-688128,-1507328,-3145728,-6815744,-14155776,
%U A179609 -30408704,-62914560,-134217728,-276824064,-587202560,-1207959552,-2550136832
%N A179609 a(n)=(5-(-1)^n-6*n)*2^(n-2).
%C A179609 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 A179609 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, -8).
%F A179609 GF(x) = (1-2*x-12*x^2)/(1-2*x-4*x^2+8*x^3)
%F A179609 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 A179609 a(n) = (5-(-1)^n-6*n)*2^(n-2)
%t A179609 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 A179609 easy,sign
%O A179609 0,3
%A A179609 _Johannes W. Meijer_, Jul 28 2010