A022322 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 8.

1, 8, 10, 19, 30, 50, 81, 132, 214, 347, 562, 910, 1473, 2384, 3858, 6243, 10102, 16346, 26449, 42796, 69246, 112043, 181290, 293334, 474625, 767960, 1242586, 2010547, 3253134, 5263682, 8516817

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},{1,8,10},40] (* Harvey P. Dale, Oct 14 2012 *)

PARI

x='x+O('x^50); Vec((1+6*x-6*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+6*x-6*x^2)/((1-x)*(1-x-x^2)).

a(n) = A022114(n) - 1. (End)

a(n) = 2*F(n+2) + 5*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017