A022321 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 7.

1, 7, 9, 17, 27, 45, 73, 119, 193, 313, 507, 821, 1329, 2151, 3481, 5633, 9115, 14749, 23865, 38615, 62481, 101097, 163579, 264677, 428257, 692935, 1121193, 1814129, 2935323, 4749453, 7684777, 12434231

Offset

0,2

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)

Formula

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

G.f.: (1+5*x-5*x^2)/((1-x)*(1-x-x^2)).

a(n) = 2*A000285(n) - 1. (End)

a(n) = 2*F(n+2) + 4*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017

Mathematica

a[0]=1; a[1]=7; a[n_]:=a[n]=a[n-1]+a[n-2]+1; Table[a[n], {n, 0, 40}] (* Harvey P. Dale, Jan 23 2011 *)

Prog

(PARI) x='x+O('x^50); Vec((1+5*x-5*x^2)/((1-x)*(1-x-x^2))) \\ G. C. Greubel, Aug 25 2017

Crossrefs

Sequence in context: A250292 A140364 A366526 * A194830 A183344 A255830

Adjacent sequences: A022318 A022319 A022320 * A022322 A022323 A022324

Keyword

nonn

Author

N. J. A. Sloane

Status

approved