A015545 Expansion of x/(1 - 5*x - 9*x^2).

0, 1, 5, 34, 215, 1381, 8840, 56629, 362705, 2323186, 14880275, 95310049, 610472720, 3910154041, 25045024685, 160416509794, 1027487771135, 6581187443821, 42153327159320, 269997322790989, 1729366558388825, 11076808697063026, 70948342510814555

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

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

Programs

Magma

[n le 2 select n-1 else 5*Self(n-1) + 9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012

Mathematica

a[n_]:=(MatrixPower[{{1,3},{1,-6}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{5, 9}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-5*x-9*x^2))) \\ G. C. Greubel, Jan 24 2018

Sage

[lucas_number1(n,5,-9) for n in range(0, 21)]# Zerinvary Lajos, Apr 24 2009

Formula

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