A022326 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 12.

1, 12, 14, 27, 42, 70, 113, 184, 298, 483, 782, 1266, 2049, 3316, 5366, 8683, 14050, 22734, 36785, 59520, 96306, 155827, 252134, 407962, 660097, 1068060, 1728158, 2796219, 4524378, 7320598, 11844977

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.: (1+10*x-10*x^2)/((1-x)*(1-x-x^2)).

a(n) = A022116(n) - 1. (End)

a(n) = 2*F(n+2) + 9*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017

a(n) = 2*a(n-1)-a(n-3). - Wesley Ivan Hurt, Apr 11 2022

Mathematica

LinearRecurrence[{2, 0, -1}, {1, 12, 14}, 50] (* G. C. Greubel, Aug 25 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1+10*x-10*x^2)/((1-x)*(1-x-x^2))) \\ G. C. Greubel, Aug 25 2017

Crossrefs

Cf. A000045, A022116.

Sequence in context: A019292 A175886 A181451 * A307167 A238228 A214504

Adjacent sequences: A022323 A022324 A022325 * A022327 A022328 A022329

Keyword

nonn

Author

N. J. A. Sloane

Status

approved