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 A015535 Expansion of x/(1 - 5*x - 2*x^2). 14

%I

%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.

%F a(n) = (1/33)*sqrt(33)*((5/2 + (1/2)*sqrt(33))^n - (5/2 - (1/2)*sqrt(33))^n). - _Paolo P. Lava_, Jan 13 2009

%t Join[{a=0,b=1},Table[c=5*b+2*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)

%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