A015529 Expansion of x/(1 - 3*x - 11*x^2).

0, 1, 3, 20, 93, 499, 2520, 13049, 66867, 344140, 1767957, 9089411, 46715760, 240130801, 1234265763, 6344236100, 32609631693, 167615492179, 861552425160, 4428427689449, 22762359745107, 116999783819260, 601385308653957, 3091153547973731

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 (3,11).

Programs

Magma

[n le 2 select n-1 else 3*Self(n-1) + 11*Self(n-2): n in [1..30] ]; // Vincenzo Librandi, Nov 12 2012

Mathematica

Join[{a=0,b=1},Table[c=3*b+11*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{3, 11}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)
CoefficientList[Series[x/(1-3x-11x^2),{x,0,30}],x] (* Harvey P. Dale, Aug 19 2024 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-3*x-11*x^2))) \\ G. C. Greubel, Jan 01 2018

Sage

[lucas_number1(n,3,-11) for n in range(0, 22)] # Zerinvary Lajos, Apr 22 2009

Formula

a(n) = 3*a(n-1) + 11*a(n-2).

a(n) = -22^n*(A^n - B^n)/sqrt(53) where A = -1/(3+sqrt(53)) and B = 1/(sqrt(53)-3). - R. J. Mathar, Apr 29 2008