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A120758 The (1,3)-entry in the matrix M^n, where M is the 3 X 3 matrix [0,2,1; 2,1,2; 1,2,2] (n>=1). 1
1, 6, 25, 116, 517, 2338, 10517, 47400, 213481, 961726, 4332145, 19515036, 87908397, 395998298, 1783838637, 8035595600, 36197658961, 163058307446, 734522939465, 3308779311556, 14904940203477, 67141752851858 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to 4.50466435...an eigenvalue of M and a root to the characteristic polynomial x^3 - 3x^2 - 7x + 1.

LINKS

Table of n, a(n) for n=1..22.

Title?, Title?

Index entries for linear recurrences with constant coefficients, signature (3,7,-1).

FORMULA

a(n)=3a(n-1)+7a(n-2)-a(n-3) (follows from the minimal polynomial of the matrix M).

G.f. x*(1+3*x) / ( 1-3*x-7*x^2+x^3 ). - R. J. Mathar, Mar 03 2013

EXAMPLE

a(7)=10517 because M^7= [6682,9842,10517;9842,14401,15438;10517,15438,16524].

MAPLE

with(linalg): M[1]:=matrix(3, 3, [0, 2, 1, 2, 1, 2, 1, 2, 2]): for n from 2 to 25 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][3, 1], n=1..25);

CROSSREFS

Cf. A120757.

Sequence in context: A094669 A100296 A346818 * A227914 A179603 A298700

Adjacent sequences:  A120755 A120756 A120757 * A120759 A120760 A120761

KEYWORD

nonn

AUTHOR

Gary W. Adamson & Roger L. Bagula, Jul 01 2006

EXTENSIONS

Corrected by T. D. Noe, Nov 07 2006

Edited by N. J. A. Sloane, Dec 04 2006

STATUS

approved

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Last modified September 18 02:31 EDT 2021. Contains 347504 sequences. (Running on oeis4.)