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A116556 a(n) = 2*a(n-1) + 2*a(n-2), a(0)=0, a(1)=4. 1

%I

%S 0,4,8,24,64,176,480,1312,3584,9792,26752,73088,199680,545536,1490432,

%T 4071936,11124736,30393344,83036160,226859008,619790336,1693298688,

%U 4626178048,12638953472,34530263040

%N a(n) = 2*a(n-1) + 2*a(n-2), a(0)=0, a(1)=4.

%D F. Albert Cotton, Chemical Applications of Group Theory, Wiley-Interscience; 3 edition (March 2, 1990).

%H G. C. Greubel, <a href="/A116556/b116556.txt">Table of n, a(n) for n = 0..1000</a>

%H Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="http://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.html">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,2).

%F a(n) = (2/sqrt(3))*( [1+sqrt(3)]^n - [1-sqrt(3)]^n ), n>=0. - _Paolo P. Lava_, Jun 10 2008

%F From _Philippe Deléham_, Nov 19 2008: (Start)

%F a(n) = 4*A002605(n).

%F G.f.: 4x/(1-2x-2x^2). (End)

%F E.g.f.: (4/sqrt(3))*exp(x)*sinh(sqrt(3)*x). - _G. C. Greubel_, Oct 31 2016

%t M = {{1, 1, 1, 1}, {1, 1, 0, 0}, {1, 0, 1, 0}, {1, 0, 0, 1}}; v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 25}]

%t LinearRecurrence[{2,2},{0,4},25] (* or *) Table[(2/sqrt(3))*( [1+sqrt(3)]^n - [1-sqrt(3)]^n ) ,{n,0,25}] (* _G. C. Greubel_, Oct 31 2016 *)

%K nonn,easy,less

%O 0,2

%A _Roger L. Bagula_, Mar 15 2006

%E Edited by _N. J. A. Sloane_, Dec 04 2006

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Last modified December 15 13:27 EST 2018. Contains 318149 sequences. (Running on oeis4.)