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%I #24 Sep 08 2022 08:45:23
%S 2,4,0,8,8,24,40,88,168,344,680,1368,2728,5464,10920,21848,43688,
%T 87384,174760,349528,699048,1398104,2796200,5592408,11184808,22369624,
%U 44739240,89478488,178956968,357913944,715827880,1431655768,2863311528
%N a(n) = abs(A154879(n+1)).
%C General form: a(n)=2^n-a(n-1). - _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008
%C For n>=1, a(n) is a(n) is the number of generalized compositions of n+3 when there are i^2-2*i-1 different types of i, (i=1,2,...). - _Milan Janjic_, Sep 24 2010
%H Vincenzo Librandi, <a href="/A115341/b115341.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F a(n) = (2^(n+1)-8*(-1)^n)/3, n>0.
%F a(n) = a(n-1) + 2*a(n-2), n>2.
%F G.f.: 2+4*x*(1-x)/((1+x)*(1-2*x)).
%t g0[n_] = 2 - Sum[(-1)^(i + 1)/Sqrt[2]^(2*i), {i, 0, n}] f[x_] = ZTransform[g0[n], n, x] g[n_] = InverseZTransform[f[1/x], x, n] a0 = Table[Abs[g[n]], {n, 1, 25}]
%t k=0;lst={k};Do[k=2^n-k;AppendTo[lst, k], {n, 3, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008 *)
%t Table[If[n==0, 2, (2^(n+1)-8*(-1)^n)/3], {n,0,30}] (* _G. C. Greubel_, Dec 30 2017 *)
%o (PARI) for(n=0,30, print1(if(n==0, 2, (2^(n+1)-8*(-1)^n)/3), ", ")) \\ _G. C. Greubel_, Dec 30 2017
%o (Magma) [2] cat [(2^(n+1)-8*(-1)^n)/3: n in [1..30]]; // _G. C. Greubel_, Dec 30 2017
%Y Cf. A001045, A078008, A097073. - _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008
%K nonn,easy,less
%O 0,1
%A _Roger L. Bagula_, Mar 06 2006
%E Edited by the Associate Editors of the OEIS, Aug 21 2009
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