A022313 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 8.

0, 8, 9, 18, 28, 47, 76, 124, 201, 326, 528, 855, 1384, 2240, 3625, 5866, 9492, 15359, 24852, 40212, 65065, 105278, 170344, 275623, 445968, 721592, 1167561, 1889154, 3056716, 4945871, 8002588, 12948460, 20951049, 33899510, 54850560, 88750071, 143600632

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, 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}, {0, 8, 9}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
RecurrenceTable[{a[0]==0,a[1]==8,a[n]==a[n-1]+a[n-2]+1},a,{n,40}] (* Harvey P. Dale, Nov 23 2017 *)

PARI

x='x+O('x^50); concat([0], Vec(x*(8-7*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*(8-7*x)/( (1-x)*(1-x-x^2) ).

a(n) = A022099(n) - 1. (End)

a(n) = F(n+2) + 7*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017