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A015574 Expansion of x/(1 - 8*x - 3*x^2). 3
0, 1, 8, 67, 560, 4681, 39128, 327067, 2733920, 22852561, 191022248, 1596735667, 13346952080, 111565823641, 932567445368, 7795237033867, 65159598607040, 544662499957921, 4552778795484488, 38056217863749667, 318108079296450800, 2659033287962855401, 22226590541592195608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths:  1, 2, 2, 4, 4, 2, 24, 4, 6, 4, 120, 4, 84, 24, 4, 8, 16, 6, 171, 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 (8,3).

FORMULA

a(n) = 8*a(n-1) + 3*a(n-2).

a(n) = (1/38)*sqrt(19)*(4+sqrt(19))^n - (1/38)*sqrt(19)*(4-sqrt(19))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b+3*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)

LinearRecurrence[{8, 3}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 8, -3) for n in xrange(0, 20)] # Zerinvary Lajos, Apr 25 2009

(MAGMA) [n le 2 select n-1 else 8*Self(n-1) + 3*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-3*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Sequence in context: A037685 A228419 A091645 * A152055 A000434 A304073

Adjacent sequences:  A015571 A015572 A015573 * A015575 A015576 A015577

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 18 16:24 EST 2018. Contains 318229 sequences. (Running on oeis4.)