A022320 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 6.

1, 6, 8, 15, 24, 40, 65, 106, 172, 279, 452, 732, 1185, 1918, 3104, 5023, 8128, 13152, 21281, 34434, 55716, 90151, 145868, 236020, 381889, 617910, 999800, 1617711, 2617512, 4235224, 6852737, 11087962

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 +4*x -4*x^2)/( (1-x)*(1-x-x^2) ).

a(n) = A022113(n) - 1. (End)

a(n) = 2*F(n+2) + 3*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017

Mathematica

LinearRecurrence[{2, 0, -1}, {1, 6, 8}, 50] (* G. C. Greubel, Aug 25 2017 *)
nxt[{a_, b_}]:={b, a+b+1}; NestList[nxt, {1, 6}, 40][[;; , 1]] (* Harvey P. Dale, Mar 29 2024 *)

Prog

(PARI) x='x+O('x^50); Vec((1 +4*x -4*x^2)/((1-x)*(1-x-x^2))) \\ G. C. Greubel, Aug 25 2017

Crossrefs

Cf. A000045.

Sequence in context: A361420 A162651 A275321 * A318387 A349908 A100646

Adjacent sequences: A022317 A022318 A022319 * A022321 A022322 A022323

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved