A015591 Expansion of x/(1 - 10*x - 9*x^2).

0, 1, 10, 109, 1180, 12781, 138430, 1499329, 16239160, 175885561, 1905008050, 20633050549, 223475577940, 2420453234341, 26215812544870, 283942204557769, 3075364358481520, 33309123425835121, 360769513484684890, 3907477245679364989, 42321698078155813900

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 2, 1, 4, 4, 2, 48, 8, 1, 4, 10, 4, 84, 48, 4, 16, 272, 2, 360, 4, ... - R. J. Mathar, Aug 10 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (10,9).

Crossrefs

Cf. A254600.

Programs

Magma

[n le 2 select n-1 else 10*Self(n-1) + 9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

Mathematica

Join[{a=0,b=1},Table[c=10*b+9*a;a=b;b=c,{n,40}]] (* Vladimir Joseph Stephan Orlovsky, Mar 29 2011 *)
LinearRecurrence[{10, 9}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)
Table[(-3 I)^(n - 1)*ChebyshevU[n - 1, 5 I/3], {n, 0, 30}] (* G. C. Greubel, Feb 13 2021 *)

Sage

[lucas_number1(n,10,-9) for n in range(0, 18)] # Zerinvary Lajos, Apr 26 2009

Formula

a(n) = 10*a(n-1) + 9*a(n-2).

a(n) = (-3*i)^(n-1) * ChebyshevU(n-1, -5*i/3). - G. C. Greubel, Feb 13 2021

Extensions

Extended by T. D. Noe, May 23 2011