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 A106567 a(0)=0, a(1)=4; for n>1, a(n) = 5*a(n-1) + 4*a(n-2). 1
 0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300, 4693957251098804, 26762888849739220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Old name was "First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,4],[1,5]] and v is the column vector [0,1]". Real Pisot roots (the eigenvalues of M): -0.701562, 5.70156. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,4). FORMULA From Chai Wah Wu, Mar 21 2018: (Start) a(n) = 5*a(n-1) + 4*a(n-2) for n > 1. G.f.: 4*x/(1 - 5*x - 4*x^2). (End) MAPLE with(linalg): M:=matrix(2, 2, [0, 4, 1, 5]): v[0]:=matrix(2, 1, [0, 1]): for n from 1 to 20 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..20); MATHEMATICA M = {{0, 4}, {1, 5}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}] CoefficientList[Series[4 x / (1 - 5 x - 4 x^2), {x, 0, 25}], x] (* Vincenzo Librandi, Mar 22 2018 *) PROG (MAGMA)  I:=[0, 4, 20]; [n le 3 select I[n] else 5*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 22 2018 (PARI) a(n) = (([0, 4; 1, 5]^n)*[0, 1]~)[1]; \\ Michel Marcus, Mar 22 2018 CROSSREFS Equals 4*A015537. Sequence in context: A192924 A258664 A231539 * A077445 A085458 A085456 Adjacent sequences:  A106564 A106565 A106566 * A106568 A106569 A106570 KEYWORD nonn AUTHOR Roger L. Bagula, May 30 2005 EXTENSIONS Edited by N. J. A. Sloane, Apr 30 2006 New name after Chai Wah Wu, by Bruno Berselli, Mar 22 2018 STATUS approved

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Last modified August 22 02:02 EDT 2018. Contains 313959 sequences. (Running on oeis4.)