A022312 a(n) = a(n-1) + a(n-2) + 1 for n>1, a(0)=0, a(1)=7.

0, 7, 8, 16, 25, 42, 68, 111, 180, 292, 473, 766, 1240, 2007, 3248, 5256, 8505, 13762, 22268, 36031, 58300, 94332, 152633, 246966, 399600, 646567, 1046168, 1692736, 2738905, 4431642, 7170548, 11602191, 18772740, 30374932, 49147673, 79522606, 128670280

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

Equals A022098(n) - 1.

G.f.: x*(7-6*x)/( (1-x)*(1-x-x^2) ). - R. J. Mathar, Apr 07 2011

a(n) = F(n+2) + 6*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017

Mathematica

LinearRecurrence[{2, 0, -1}, {0, 7, 8}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x*(7-6*x)/( (1-x)*(1-x-x^2) ))) \\ G. C. Greubel, Aug 25 2017

Crossrefs

Cf. A000045.

Sequence in context: A318613 A127933 A006878 * A351087 A055661 A287334

Adjacent sequences: A022309 A022310 A022311 * A022313 A022314 A022315

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved