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A106567 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]. 0
0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Real Pisot roots (the eigenvalues of M): -0.701562, 5.70156.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, 4], [1, 5]] and v[0] is the column vector [0,1].

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}]

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

STATUS

approved

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Last modified February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)