A122994 a(n) = a(n-1)+9*a(n-2) initialized with a(0)=1, a(1)=3.

1, 3, 12, 39, 147, 498, 1821, 6303, 22692, 79419, 283647, 998418, 3551241, 12537003, 44498172, 157331199, 557814747, 1973795538, 6994128261, 24758288103, 87705442452, 310530035379, 1099879017447, 3894649335858, 13793560492881, 48845404515603, 172987448951532

Offset

0,2

Comments

The two roots of the denominator of the g.f. (for Binet's formula) are -0.393486... and 0.2823756...

Pisano period lengths: 1, 3, 1, 6, 6, 3, 6, 12, 1, 6, 10, 6, 84, 6, 6, 24,144, 3, 72, 6,... - R. J. Mathar, Aug 10 2012

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1,9).

Formula

G.f.: -(1+2*x)/(-1+x+9*x^2). a(n) = A015445(n)+2*A015445(n-1). [R. J. Mathar, Aug 12 2009]

a(n) = (1/2+5*sqrt(37)/74) *(1/2+sqrt(37)/2)^(n-1) +(1/2-5*sqrt(37)/74) *(1/2-sqrt(37)/2)^(n-1). [Antonio Alberto Olivares, Jun 07 2011]

a(n) = Sum_{k, 0<=k<=n} A103631(n,k)*3^k. - Philippe Deléham, Dec 17 2011

a(n) = A015445(n) + 2*A015445(n-1), n>0. - Ralf Stephan, Jul 21 2013

Mathematica

CoefficientList[Series[(-2 z - 1)/(9 z^2 + z - 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

Crossrefs

Cf. A026597.

Sequence in context: A110153 A343360 A183366 * A271218 A062311 A303348

Adjacent sequences: A122991 A122992 A122993 * A122995 A122996 A122997

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 22 2006

Extensions

Definition replaced with the Deleham recurrence of Mar 2009 by the Assoc. Editors of the OEIS, Mar 12 2010

Status

approved