A022315 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 10.

0, 10, 11, 22, 34, 57, 92, 150, 243, 394, 638, 1033, 1672, 2706, 4379, 7086, 11466, 18553, 30020, 48574, 78595, 127170, 205766, 332937, 538704, 871642, 1410347, 2281990, 3692338, 5974329, 9666668

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

CoefficientList[Series[(10 x-9 x^2)/(1-2 x+x^3),{x,0,30}],x]  (* Harvey P. Dale, Mar 05 2011 *)

PARI

x='x+O('x^50); concat([0], Vec(x*(10-9*x)/( (1-x)*(1-x-x^2) ))) \\ G. C. Greubel, Aug 25 2017

Formula

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

G.f.: x*(10-9*x)/( (1-x)*(1-x-x^2) ).

a(n) = A022101(n) - 1. (End)

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