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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 May 24 07:07 EDT 2018. Contains 304500 sequences. (Running on oeis4.)