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

0,3

Comments

This is the Lucas sequence U(5,-3). - Bruno Berselli, Jan 09 2013

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).

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)

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 *)

Prog

(Sage) [lucas_number1(n, 5, -3) for n in range(0, 22)] # Zerinvary Lajos, Apr 24 2009
(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
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-3*x^2))) \\ G. C. Greubel, Jan 01 2018

Crossrefs

Sequence in context: A126699 A267828 A164537 * A271808 A005785 A027912

Adjacent sequences: A015533 A015534 A015535 * A015537 A015538 A015539

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved