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A122885 The (3,3)-entry in the n-th power of the 3 X 3 matrix M = [1,1,1; 4,2,1; 9,3,1]. 3
1, 13, 61, 385, 2185, 12853, 74677, 435721, 2538625, 14798077, 86245741, 502684561, 2929845241, 17076419653, 99528607141, 580095354265, 3381043256305, 19706164707853, 114855943942237, 669429501042721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (4, 11, -2).

FORMULA

a(n+1) = 4*a(n) + 11*a(n-1) - 2*a(n-2).

a(n)=-(45/68)*sqrt(2)*[3-2*sqrt(2)]^(n-1)+(33/34)*[3+2*sqrt(2)]^(n-1)+(45/ 68)*[3+2*sqrt(2)]^(n-1) *sqrt(2)+(33/34)*[3-2*sqrt(2)]^(n-1)-(16/ 17)*(-2)^(n-1), with n>=1 - Paolo P. Lava, Jul 09 2008

G.f.: x*(1+9*x-2*x^2)/((2*x+1) * (1-6*x+x^2)). [From R. J. Mathar, Aug 12 2009]

EXAMPLE

M^2 * [0,0,1] = [3, 7, 13], so the right term in the last row is 13 = a(2).

CROSSREFS

Cf. A122883, A122884, A122886.

Sequence in context: A141725 A279762 A147185 * A257216 A135535 A158870

Adjacent sequences:  A122882 A122883 A122884 * A122886 A122887 A122888

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson and Roger L. Bagula, Sep 17 2006

EXTENSIONS

More terms from Paolo P. Lava, Jul 09 2008

Definition replaced by a precise phrase by the Assoc. Editors of the OEIS, Mar 12 2010.

STATUS

approved

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Last modified June 30 09:38 EDT 2022. Contains 354920 sequences. (Running on oeis4.)