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%I #34 Sep 08 2022 08:45:54
%S 0,1,4,24,128,704,3840,20992,114688,626688,3424256,18710528,102236160,
%T 558628864,3052404736,16678649856,91133837312,497964548096,
%U 2720928890880,14867431948288,81237158920192,443888091267072,2425449636429824,13252903275855872
%N a(n) = 4*a(n-1) + 8*a(n-2), with a(1)=0 and a(2)=1.
%H Nathaniel Johnston, <a href="/A180222/b180222.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,8).
%F a(n) = 2^(n-3)*((1+sqrt(3))^(n-1)-(1-sqrt(3))^(n-1))/sqrt(3). - _Rolf Pleisch_, May 14 2011
%F a(n) = (-1)^n*A174443(n-1). - _Nathaniel Johnston_, May 14 2011
%F G.f.: x^2/(1-4*x-8*x^2).
%F a(n+2) = Sum_{k=0..n} A201947(n,k)*3^(n-k). - _Philippe Deléham_, Dec 07 2011
%F a(n+2) = 2^n*A002605(n+1). - _R. J. Mathar_, May 07 2019
%t Join[{a=0,b=1},Table[c=4*b+8*a;a=b;b=c,{n,100}]]
%t LinearRecurrence[{4,8}, {0,1}, 30] (* _G. C. Greubel_, Jan 16 2018 *)
%o (PARI) concat(0,Vec(1/(1-4*x-8*x^2)+O(x^98))) \\ _Charles R Greathouse IV_, Dec 07 2011
%o (Magma) I:=[0,1]; [n le 2 select I[n] else 4*Self(n-1) + 8*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 16 2018
%K nonn,easy
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011
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