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 A106568 Expansion of 4*x/(1-4*x-4*x^2). 0
 0, 4, 16, 80, 384, 1856, 8960, 43264, 208896, 1008640, 4870144, 23515136, 113541120, 548225024, 2647064576, 12781158400, 61712891904, 297976201216, 1438756372480, 6946930294784, 33542746669056, 161958707855360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Previous name was: First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,4],[1,4]] and v is the column vector [0,1]. LINKS Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (4,4). FORMULA a(n) = 4 * A057087(n). a(n) = A094013(n+1). - R. J. Mathar, Aug 24 2008 From Philippe Deléham, Sep 19 2009: (Start) a(n) = 4*a(n-1) + 4*a(n-2) for n > 2; a(0) = 0, a(1)=4. G.f.: 4x/(1-4x-4x^2). (End) G.f.: Q(0) - 1, where Q(k) = 1 + 2*(1+2*x)*x + 2*(2*k+3)*x - 2*x*(2*k+1 +2*x+1)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013 MAPLE with(linalg): M:=matrix(2, 2, [0, 4, 1, 4]): v[0]:=matrix(2, 1, [0, 1]): for n from 1 to 23 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..23); MATHEMATICA M = {{0, 4}, {1, 4}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}] CROSSREFS Cf. A009013. Sequence in context: A081682 A068788 A094013 * A183146 A160564 A075581 Adjacent sequences:  A106565 A106566 A106567 * A106569 A106570 A106571 KEYWORD nonn,easy,less AUTHOR Roger L. Bagula, May 30 2005 EXTENSIONS Edited by N. J. A. Sloane, Apr 30 2006 Simpler name using o.g.f. by Joerg Arndt, Oct 05 2013 STATUS approved

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Last modified November 30 04:01 EST 2020. Contains 338781 sequences. (Running on oeis4.)