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%I #30 Sep 08 2022 08:44:40
%S 0,1,4,25,136,769,4300,24121,135184,757825,4247956,23812249,133480600,
%T 748232641,4194255964,23511117625,131792774176,738771155329,
%U 4141219588900,23213818753561,130126251314344,729429374039425,4088853757986796,22920279398302009
%N a(n) = 4*a(n-1) + 9*a(n-2).
%C For n>=2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 4's along the main diagonal, and 3's along the superdiagonal and the subdiagonal. - _John M. Campbell_, Jul 19 2011
%H Vincenzo Librandi, <a href="/A015533/b015533.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,9).
%F From _R. J. Mathar_, Apr 29 2008: (Start)
%F O.g.f.: x/(1-4*x-9*x^2).
%F a(n) = -9^n*(A^n - B^n)/(2*sqrt(13)) where A = -1/(2+sqrt(13)) and B = 1/(sqrt(13)-2). (End)
%F a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*3^(n-k), n>=1. - _Philippe Deléham_, Jan 27 2009
%t a[n_]:=(MatrixPower[{{1,4},{1,-5}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)
%t LinearRecurrence[{4, 9}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)
%o (Sage) [lucas_number1(n,4,-9) for n in range(0, 22)] # _Zerinvary Lajos_, Apr 23 2009
%o (Magma) [n le 2 select n-1 else 4*Self(n-1)+9*Self(n-2): n in [1..30] ]; // _Vincenzo Librandi_, Nov 12 2012
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-4*x-9*x^2))) \\ _G. C. Greubel_, Jan 01 2018
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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