A015548 Expansion of x/(1 - 5*x - 12*x^2).

0, 1, 5, 37, 245, 1669, 11285, 76453, 517685, 3505861, 23741525, 160777957, 1088788085, 7373275909, 49931836565, 338138493733, 2289874507445, 15507034462021, 105013666399445, 711152745541477, 4815927724500725, 32613471569001349

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 (5,12).

Crossrefs

Cf. A015564 (binomial transform).

Programs

Magma

[n le 2 select n-1 else 5*Self(n-1) + 12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012

Mathematica

Join[{a=0,b=1},Table[c=5*b+12*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{5, 12}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)
CoefficientList[Series[x/(1-5x-12x^2),{x,0,30}],x] (* Harvey P. Dale, May 27 2023 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-5*x-12*x^2))) \\ G. C. Greubel, Jan 16 2018

Sage

[lucas_number1(n,5,-12) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

a(n) = 2*A099919(n-1) + 1, for n>=1.

a(n) = 5 a(n-1) + 12 a(n-2).