A015524 a(n) = 3*a(n-1) + 7*a(n-2).

0, 1, 3, 16, 69, 319, 1440, 6553, 29739, 135088, 613437, 2785927, 12651840, 57457009, 260933907, 1185000784, 5381539701, 24439624591, 110989651680, 504046327177, 2289066543291, 10395523920112, 47210037563373

Offset

0,3

Comments

Linear 2nd order recurrence.

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,7).

Formula

From R. J. Mathar, Apr 21 2008: (Start)

O.g.f.: x/(1 - 3*x - 7*x^2).

a(n) = 14^n*(1/A^n -(-1)^n/B^n)/sqrt(37), where A = sqrt(37) - 3 = A010491 - 3 and B = sqrt(37) + 3 = A010491 + 3. (End)

a(n) = (7*(111+23*sqrt(37))*(1/2*(3+sqrt(37)))^n + (2553 + 431*sqrt(37)) * (1/2 (3-sqrt(37)))^n)/(518*(45+8*sqrt(37))). - Harvey P. Dale, Jul 04 2011

Mathematica

a[n_]:=(MatrixPower[{{1, 3}, {1, -4}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{3, 7}, {0, 1}, 30] (* Harvey P. Dale, Jul 04 2011 *)

Prog

(Sage) [lucas_number1(n, 3, -7) for n in range(0, 23)] #  Zerinvary Lajos, Apr 22 2009
(Magma) [n le 2 select n-1 else 3*Self(n-1)+7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 3*x - 7*x^2))) \\ G. C. Greubel, Jan 01 2018

Crossrefs

Sequence in context: A000269 A370248 A370274 * A012279 A037098 A316170

Adjacent sequences: A015521 A015522 A015523 * A015525 A015526 A015527

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved