A167030 - OEIS

%I #35 Sep 08 2022 08:45:48

%S -1,0,0,2,4,10,20,42,84,170,340,682,1364,2730,5460,10922,21844,43690,

%T 87380,174762,349524,699050,1398100,2796202,5592404,11184810,22369620,

%U 44739242,89478484,178956970,357913940,715827882

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

%H G. C. Greubel, <a href="/A167030/b167030.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..240 from Vincenzo Librandi)

%H Nicolas Gastineau and O. Togni, <a href="https://arxiv.org/abs/1711.10906">On S-packing edge-colorings of cubic graphs</a>, arXiv preprint arXiv:1711.10906 [cs.DM], 2017.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

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

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

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

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

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

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

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

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

%F E.g.f.: (1/3)*(exp(2*x) - 3*exp(x) - exp(-x)). - _G. C. Greubel_, May 30 2016

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

%o (Magma) [(2^n-(-1)^n)/3 -1: n in [0..40] ]; // _Vincenzo Librandi_, Apr 28 2011

%o (PARI) a(n)=(2^n-(-1)^n)/3-1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y A026644 is an essentially identical sequence.

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

%K sign,easy

%O 0,4

%A _Paul Curtz_, Oct 27 2009

%E Edited by _R. J. Mathar_, Dec 17 2010