A022323 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 9.

1, 9, 11, 21, 33, 55, 89, 145, 235, 381, 617, 999, 1617, 2617, 4235, 6853, 11089, 17943, 29033, 46977, 76011, 122989, 199001, 321991, 520993, 842985, 1363979, 2206965, 3570945, 5777911, 9348857

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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).

Programs

Mathematica

LinearRecurrence[{2,0,-1}, {1,9,11}, 50] (* G. C. Greubel, Aug 25 2017 *)

PARI

x='x+O('x^50); Vec((1+7*x-7*x^2)/((1-x)*(1-x-x^2))) \\ G. C. Greubel, Aug 25 2017

Formula

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

G.f.: (1+7*x-7*x^2)/((1-x)*(1-x-x^2)).

a(n) = A022367(n) - 1. (End)

a(n) = 2*F(n+2) + 6*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017