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A015536 Expansion of x/(1-5*x-3*x^2). 13
0, 1, 5, 28, 155, 859, 4760, 26377, 146165, 809956, 4488275, 24871243, 137821040, 763718929, 4232057765, 23451445612, 129953401355, 720121343611, 3990466922120, 22112698641433, 122534893973525, 679012565791924, 3762667510880195, 20850375251776747 (list; graph; refs; listen; history; text; internal format)
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 to sequences with 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.

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). - Paul Barry, Jul 20 2004

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 xrange(0, 22)]# [From 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

CROSSREFS

Sequence in context: A037682 A126699 A164537 * A005785 A027912 A243669

Adjacent sequences:  A015533 A015534 A015535 * A015537 A015538 A015539

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 20 11:26 EST 2014. Contains 252241 sequences.