A167030 a(n) = (2^n - (-1)^n - 3)/3.

-1, 0, 0, 2, 4, 10, 20, 42, 84, 170, 340, 682, 1364, 2730, 5460, 10922, 21844, 43690, 87380, 174762, 349524, 699050, 1398100, 2796202, 5592404, 11184810, 22369620, 44739242, 89478484, 178956970, 357913940, 715827882

Offset: 0

Author

Paul Curtz, Oct 27 2009

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..240 from Vincenzo Librandi)
• Nicolas Gastineau and O. Togni, On S-packing edge-colorings of cubic graphs, arXiv preprint arXiv:1711.10906 [cs.DM], 2017.
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

A026644 is an essentially identical sequence.

Cf. A001045, A153772, A047849, A020988, A000975.

Programs

Magma

[(2^n-(-1)^n)/3 -1: n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011

Mathematica

f[n_] := (2^n - (-1)^n - 3)/3; Array[f, 32, 0]

PARI

a(n)=(2^n-(-1)^n)/3-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = A001045(n) - 1.

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).

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

2*a(n) = A153772(n+1).

a(2n+1) - a(2n) = A047849(n).

a(2n+1) = A020988(n); a(2n+2) = 2*A020988(n).

a(n+2) = 2*A000975(n).

a(2n+2) = a(2n) + 2^(2n).

E.g.f.: (1/3)*(exp(2*x) - 3*exp(x) - exp(-x)). - G. C. Greubel, May 30 2016

Extensions

Edited by R. J. Mathar, Dec 17 2010