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

%I A106434 #41 Jan 01 2024 11:37:09
%S A106434 0,2,6,22,78,278,990,3526,12558,44726,159294,567334,2020590,7196438,
%T A106434 25630494,91284358,325114062,1157910902,4123960830,14687704294,
%U A106434 52311034542,186308512214,663547605726,2363259841606,8416874736270,29977143892022,106765181148606
%N A106434 The (1,1)-entry of the matrix A^n, where A = [0,1;2,3].
%H A106434 Vincenzo Librandi, <a href="/A106434/b106434.txt">Table of n, a(n) for n = 1..1000</a>
%H A106434 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,2).
%F A106434 a(n) = 3*a(n-1) + 2*a(n-2) for n>=3; a(1)=0, a(2)=2.
%F A106434 O.g.f.: 2*x^2/(1-3*x-2*x^2). - _R. J. Mathar_, Dec 05 2007
%F A106434 a(n) = 2 * A007482(n-2) for n >= 2.
%p A106434 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);
%t A106434 LinearRecurrence[{3, 2}, {0, 2}, 50] (* _Vladimir Joseph Stephan Orlovsky_, Feb 24 2012 *)
%o A106434 (PARI) A106434(n)=([0,1;2,3]^n)[1,1] /* _M. F. Hasler_, Dec 01 2008 */
%Y A106434 Cf. A028860, A100638.
%K A106434 nonn,easy,less
%O A106434 1,2
%A A106434 _Roger L. Bagula_, May 29 2005
%E A106434 Simplified definition and added cross reference. - _M. F. Hasler_, Dec 01 2008
%E A106434 Edited by _N. J. A. Sloane_, May 20 2006 and Dec 04 2008