A015587 Expansion of x/(1 - 9*x - 11*x^2).

0, 1, 9, 92, 927, 9355, 94392, 952433, 9610209, 96968644, 978430095, 9872525939, 99615464496, 1005136965793, 10142002801593, 102334531838060, 1032572817360063, 10418835206459227, 105127817849093736, 1060757547912895121, 10703223927556087185, 107997348375046630996

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 3, 4, 6, 20, 12, 48, 6, 12, 60, 5, 12,168, 48, 20, 12,288, 12, 6, 60,... - 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 (9,11).

Programs

Magma

[n le 2 select n-1 else 9*Self(n-1) + 11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

Mathematica

Join[{a=0,b=1},Table[c=9*b+11*a;a=b;b=c,{n,40}]] (* Vladimir Joseph Stephan Orlovsky, Mar 29 2011 *)
LinearRecurrence[{9, 11}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-9*x-11*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

[lucas_number1(n,9,-11) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009

Formula

a(n) = 9*a(n-1) + 11*a(n-2).