A015536 Expansion of x/(1-5*x-3*x^2).
0, 1, 5, 28, 155, 859, 4760, 26377, 146165, 809956, 4488275, 24871243, 137821040, 763718929, 4232057765, 23451445612, 129953401355, 720121343611, 3990466922120, 22112698641433, 122534893973525, 679012565791924, 3762667510880195, 20850375251776747
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Wikipedia, Lucas sequence: Specific names.
- Index entries for linear recurrences with constant coefficients, signature (5,3).
Programs
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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
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Mathematica
Join[{a=0,b=1},Table[c=5*b+3*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *) LinearRecurrence[{5, 3}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *) -
PARI
x='x+O('x^30); concat([0], Vec(x/(1-5*x-3*x^2))) \\ G. C. Greubel, Jan 01 2018 -
Sage
[lucas_number1(n,5,-3) for n in range(0, 22)] # Zerinvary Lajos, Apr 24 2009
Formula
a(n) = 5*a(n-1) + 3*a(n-2) with n > 1, a(0)=0, a(1)=1.
From Paul Barry, Jul 20 2004: (Start)
a(n) = (5/2 + sqrt(37)/2)^n/sqrt(37) - (5/2 - sqrt(37)/2)^n/sqrt(37).
a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k)3^k*5^(n-2k-1). (End)
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