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A015576 Expansion of x/(1 - 8*x - 7*x^2). 3
0, 1, 8, 71, 624, 5489, 48280, 424663, 3735264, 32854753, 288984872, 2541862247, 22357792080, 196655372369, 1729747523512, 15214567794679, 133824775022016, 1177100174738881, 10353574823065160, 91068299807693447, 801021422223003696, 7045649476437883697, 61972345767064095448 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 2, 8, 4, 24, 8, 1, 4, 24, 24, 5, 8, 12, 2, 24, 4, 96, 24, 18, 24, ... - 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 (8,7).

FORMULA

a(n) = 8*a(n-1) + 7*a(n-2).

a(n) = (1/46)*(4+sqrt(23))^n*sqrt(23) - (1/46)*(4-sqrt(23))^n*sqrt(23), with n >= 0. - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b+7*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)

LinearRecurrence[{8, 7}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 8, -7) for n in xrange(0, 20)] # Zerinvary Lajos, Apr 25 2009

(MAGMA) [n le 2 select n-1 else 8*Self(n-1) + 7*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-7*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Sequence in context: A038145 A198856 A320092 * A070998 A187709 A292865

Adjacent sequences:  A015573 A015574 A015575 * A015577 A015578 A015579

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)