

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
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OFFSET

1,2


COMMENTS

a(n)/a(n1) 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(n1)+7a(n2)a(n3) (follows from the minimal polynomial of the matrix M).
G.f. x*(1+3*x) / ( 13*x7*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[n1]) od: seq(M[n][3, 1], n=1..25);


CROSSREFS

Cf. A120757.
Sequence in context: A295202 A094669 A100296 * 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



