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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,2).
Programs
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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);
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Mathematica
LinearRecurrence[{3, 2}, {0, 2}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *) -
PARI
A106434(n)=([0,1;2,3]^n)[1,1] /* M. F. Hasler, Dec 01 2008 */
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.
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