A015581 a(n) = 9*a(n-1) + 5*a(n-2).

0, 1, 9, 86, 819, 7801, 74304, 707741, 6741189, 64209406, 611590599, 5825362421, 55486214784, 528502745161, 5033955780369, 47948115749126, 456702820643979, 4350065964541441, 41434107784092864, 394657299879542981, 3759086237836351149, 35805062639924875246

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

A linear 2nd-order recurrence.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,5).

Crossrefs

Cf. A015579, A099371.

Programs

Magma

[n le 2 select n-1 else 9*Self(n-1) + 5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

Mathematica

Join[{a=0,b=1},Table[c=9*b+5*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
LinearRecurrence[{9, 5}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-9*x-5*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

[lucas_number1(n,9,-5) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009

Formula

G.f.: x/(1 - 9*x - 5*x^2). - R. J. Mathar, Dec 02 2007

Extensions

Extended by T. D. Noe, May 23 2011