A022311 a(n) = a(n-1) + a(n-2) + 1 for n>1, a(0)=0, a(1)=1.

0, 6, 7, 14, 22, 37, 60, 98, 159, 258, 418, 677, 1096, 1774, 2871, 4646, 7518, 12165, 19684, 31850, 51535, 83386, 134922, 218309, 353232, 571542, 924775, 1496318, 2421094, 3917413, 6338508, 10255922, 16594431, 26850354, 43444786, 70295141, 113739928

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1)

Crossrefs

Cf. A000045.

Programs

Mathematica

LinearRecurrence[{2, 0, -1}, {0, 6, 7}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)

PARI

x='x+O('x^50); concat([0],Vec((6*x-5*x^2)/(1-2*x+x^3))) \\ G. C. Greubel, Aug 25 2017

Formula

Equals A022097(n) - 1.

G.f.: (6*x-5*x^2)/(1-2*x+x^3). - Franklin T. Adams-Watters, Oct 17 2006

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