A022317 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 12.

0, 12, 13, 26, 40, 67, 108, 176, 285, 462, 748, 1211, 1960, 3172, 5133, 8306, 13440, 21747, 35188, 56936, 92125, 149062, 241188, 390251, 631440, 1021692, 1653133, 2674826, 4327960, 7002787, 11330748

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Formula

From R. J. Mathar, Apr 07 2011: (Start)

G.f.: x*(12-11*x)/( (1-x)*(1-x-x^2) ).

a(n) = A022103(n) - 1. (End)

a(n) = F(n+2) + 11*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017

Mathematica

LinearRecurrence[{2, 0, -1}, {0, 12, 13}, 50] (* G. C. Greubel, Aug 25 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x*(12-11*x)/( (1-x)*(1-x-x^2) ))) \\ G. C. Greubel, Aug 25 2017

Crossrefs

Sequence in context: A041290 A041288 A042207 * A125998 A307279 A106323

Adjacent sequences: A022314 A022315 A022316 * A022318 A022319 A022320

Keyword

nonn

Author

N. J. A. Sloane

Status

approved