A015580 Expansion of x/(1 - 9*x - 4*x^2).

0, 1, 9, 85, 801, 7549, 71145, 670501, 6319089, 59553805, 561260601, 5289560629, 49851088065, 469818035101, 4427766668169, 41729172153925, 393273616058001, 3706379233137709, 34930507562471385, 329200084994793301, 3102522795203025249, 29239505496806400445

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 1, 2, 1, 3, 2, 48, 2, 6, 3, 10, 2, 42, 48, 6, 4, 24, 6,360, 3, ... - 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 (9,4)

Crossrefs

Cf. A015579, A099371.

Programs

Magma

[n le 2 select n-1 else 9*Self(n-1) + 4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

LinearRecurrence[{9, 4}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-9*x-4*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

[lucas_number1(n,9,-4) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009

Formula

a(n) = 9*a(n-1) + 4*a(n-2).

Extensions

Extended by T. D. Noe, May 23 2011