The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A106434 The (1,1)-entry of the matrix A^n, where A = [0,1;2,3]. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The characteristic polynomial of the matrix A is x^2-3x-2. The first entry of the vector v[n]=A*v[n-1], where A is the 2 X 2 matrix [[0,2],[1,3]] and v is the column vector [0,1]. The (1,1)-entry of the matrix A^n where A=[0,1,1;1,2,1;1,1,2]. - David Neil McGrath, Jul 18 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,2). FORMULA Recurrence relation: a(n)=3a(n-1)+2a(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) = -(2/17)*sqrt(17)*[3/2-(1/2)*sqrt(17)]^n+(2/17)*[3/2+(1/2)*sqrt(17)]^n*sqrt(17), with n>=0. - Paolo P. Lava, Jun 12 2008 MAPLE a:=0: a:=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 M = {{0, 2}, {1, 3}} v = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][]], {n, 1, 50}] (* or *) 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. Equals 2*A007482(n-2), for n>1. Sequence in context: A148496 A217528 A181367 * A150228 A203038 A206304 Adjacent sequences:  A106431 A106432 A106433 * A106435 A106436 A106437 KEYWORD nonn,easy 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)