A015576 Expansion of x/(1 - 8*x - 7*x^2).

0, 1, 8, 71, 624, 5489, 48280, 424663, 3735264, 32854753, 288984872, 2541862247, 22357792080, 196655372369, 1729747523512, 15214567794679, 133824775022016, 1177100174738881, 10353574823065160, 91068299807693447, 801021422223003696, 7045649476437883697, 61972345767064095448

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

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).

Programs

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

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 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-8*x-7*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

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

Formula

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