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

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,12).

Formula

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

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

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 *)

Prog

(Sage) [lucas_number1(n, 5, -12) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(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
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-12*x^2))) \\ G. C. Greubel, Jan 16 2018

Crossrefs

Cf. A015564 (binom. transf.)

Sequence in context: A088582 A088583 A202556 * A183385 A054417 A080507

Adjacent sequences: A015545 A015546 A015547 * A015549 A015550 A015551

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved