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a(n) = 4*a(n-1) + 7*a(n-2).
12

%I #29 Sep 08 2022 08:44:40

%S 0,1,4,23,120,641,3404,18103,96240,511681,2720404,14463383,76896360,

%T 408829121,2173591004,11556167863,61439808480,326652408961,

%U 1736688295204,9233320043543,49090098240600,260993633267201,1387605220753004,7377376315882423

%N a(n) = 4*a(n-1) + 7*a(n-2).

%C Pisano period lengths: 1, 2, 8, 4, 4, 8, 3, 4, 24, 4, 110, 8, 168, 6, 8, 8, 288, 24, 18, 4, ... . - _R. J. Mathar_, Aug 10 2012

%H Vincenzo Librandi, <a href="/A015532/b015532.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 (4,7).

%F From _R. J. Mathar_, Apr 29 2008: (Start)

%F O.g.f.: x/(1 - 4*x - 7*x^2).

%F a(n) = -7^n*(A^n - B^n)/(2*sqrt(11)) where A = -1/(2+sqrt(11)) and B = 1/(sqrt(11)-2). (End)

%t a[n_]:=(MatrixPower[{{1,2},{1,-5}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)

%t LinearRecurrence[{4, 7}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)

%o (Sage) [lucas_number1(n,4,-7) for n in range(0, 21)]# _Zerinvary Lajos_, Apr 23 2009

%o (Magma) [n le 2 select n-1 else 4*Self(n-1)+7*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-7*x^2))) \\ _G. C. Greubel_, Jan 01 2018

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_