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%I #35 Sep 08 2022 08:44:40
%S 0,1,5,28,155,859,4760,26377,146165,809956,4488275,24871243,137821040,
%T 763718929,4232057765,23451445612,129953401355,720121343611,
%U 3990466922120,22112698641433,122534893973525,679012565791924,3762667510880195,20850375251776747
%N Expansion of x/(1-5*x-3*x^2).
%C This is the Lucas sequence U(5,-3). - _Bruno Berselli_, Jan 09 2013
%H Vincenzo Librandi, <a href="/A015536/b015536.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 (5,3).
%F a(n) = 5*a(n-1) + 3*a(n-2) with n > 1, a(0)=0, a(1)=1.
%F From _Paul Barry_, Jul 20 2004: (Start)
%F a(n) = (5/2 + sqrt(37)/2)^n/sqrt(37) - (5/2 - sqrt(37)/2)^n/sqrt(37).
%F a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k)3^k*5^(n-2k-1). (End)
%t Join[{a=0,b=1},Table[c=5*b+3*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)
%t LinearRecurrence[{5, 3}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)
%o (Sage) [lucas_number1(n,5,-3) for n in range(0, 22)] # _Zerinvary Lajos_, Apr 24 2009
%o (Magma) [n le 2 select n-1 else 5*Self(n-1)+3*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-3*x^2))) \\ _G. C. Greubel_, Jan 01 2018
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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