A015574 Expansion of x/(1 - 8*x - 3*x^2).

0, 1, 8, 67, 560, 4681, 39128, 327067, 2733920, 22852561, 191022248, 1596735667, 13346952080, 111565823641, 932567445368, 7795237033867, 65159598607040, 544662499957921, 4552778795484488, 38056217863749667, 318108079296450800, 2659033287962855401, 22226590541592195608

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

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).

Programs

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

Mathematica

LinearRecurrence[{8, 3}, {0, 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

Sage

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

Formula

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