A106434 The (1,1)-entry of the matrix A^n, where A = [0,1;2,3].

0, 2, 6, 22, 78, 278, 990, 3526, 12558, 44726, 159294, 567334, 2020590, 7196438, 25630494, 91284358, 325114062, 1157910902, 4123960830, 14687704294, 52311034542, 186308512214, 663547605726, 2363259841606, 8416874736270, 29977143892022, 106765181148606

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,2).

Formula

a(n) = 3*a(n-1) + 2*a(n-2) for n>=3; a(1)=0, a(2)=2.

O.g.f.: 2*x^2/(1-3*x-2*x^2). - R. J. Mathar, Dec 05 2007

a(n) = 2 * A007482(n-2) for n >= 2.

Maple

a[1]:=0: a[2]:=2: for n from 3 to 25 do a[n]:=3*a[n-1]+2*a[n-2] od: seq(a[n], n=1..25);

Mathematica

LinearRecurrence[{3, 2}, {0, 2}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *)

Prog

(PARI) A106434(n)=([0, 1; 2, 3]^n)[1, 1] /* M. F. Hasler, Dec 01 2008 */

Crossrefs

Cf. A028860, A100638.

Sequence in context: A148496 A217528 A181367 * A150228 A203038 A206304

Adjacent sequences: A106431 A106432 A106433 * A106435 A106436 A106437

Keyword

nonn,easy,less

Author

Roger L. Bagula, May 29 2005

Extensions

Simplified definition and added cross reference. - M. F. Hasler, Dec 01 2008

Edited by N. J. A. Sloane, May 20 2006 and Dec 04 2008

Status

approved