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%I #53 Dec 18 2023 12:18:23
%S 0,1,5,27,145,779,4185,22483,120785,648891,3486025,18727907,100611585,
%T 540513739,2903791865,15599986803,83807517745,450237562331,
%U 2418802847145,12994489360387,69810052496225,375039241201899,2014816311001945,10824160037413523
%N Expansion of x/(1 - 5*x - 2*x^2).
%C Pisano period lengths: 1, 1, 3, 2, 8, 3, 48, 2, 3, 8, 110, 6, 168, 48, 24, 4, 8, 3, 45, 8, ... - _R. J. Mathar_, Aug 10 2012
%C This is the Lucas sequence U(5,-2). - _Bruno Berselli_, Jan 08 2013
%C For n > 0, a(n) equals the number of words of length n-1 over {0,1,...,6} in which 0 and 1 avoid runs of odd lengths. - _Milan Janjic_, Jan 08 2017
%H Vincenzo Librandi, <a href="/A015535/b015535.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lucas_sequence#Specific_names">Lucas sequence: Specific names</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,2).
%F a(n) = 5*a(n-1) + 2*a(n-2) with n > 1, a(0)=0, a(1)=1.
%t LinearRecurrence[{5, 2}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)
%o (Sage) [lucas_number1(n,5,-2) for n in range(0, 22)] # _Zerinvary Lajos_, Apr 24 2009
%o (Magma) [n le 2 select n-1 else 5*Self(n-1)+2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2012
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-2*x^2))) \\ _G. C. Greubel_, Jan 01 2018
%Y Cf. A201002 (prime subsequence).
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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