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A015575 Expansion of x/(1 - 8*x - 5*x^2). 3
0, 1, 8, 69, 592, 5081, 43608, 374269, 3212192, 27568881, 236612008, 2030740469, 17428983792, 149585572681, 1283829500408, 11018563866669, 94567658435392, 811634086816481, 6965910986708808, 59785458327752869, 513113221555566992, 4403833064083300281, 37796230620444237208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 2, 3, 2, 4, 6, 21, 4, 9, 4, 120, 6, 56, 42, 12, 8, 16, 18, 360, 4, ... - R. J. Mathar, Aug 10 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,5).

FORMULA

a(n) = 8*a(n-1) + 5*a(n-2).

a(n) = (1/42)*(4+sqrt(21))^n*sqrt(21) - (1/42)*sqrt(21)*(4-sqrt(21))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b+5*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)

LinearRecurrence[{8, 5}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 8, -5) for n in xrange(0, 20)] # Zerinvary Lajos, Apr 25 2009

(MAGMA) [n le 2 select n-1 else 8*Self(n-1) + 5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-8*x-5*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Sequence in context: A178368 A297633 A152279 * A214344 A228421 A152109

Adjacent sequences:  A015572 A015573 A015574 * A015576 A015577 A015578

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 22 22:08 EDT 2018. Contains 305673 sequences. (Running on oeis4.)