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A116556 a(n) = 2*a(n-1) + 2*a(n-2), a(0)=0, a(1)=4. 1
0, 4, 8, 24, 64, 176, 480, 1312, 3584, 9792, 26752, 73088, 199680, 545536, 1490432, 4071936, 11124736, 30393344, 83036160, 226859008, 619790336, 1693298688, 4626178048, 12638953472, 34530263040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (2,2).

FORMULA

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

From Philippe Deléham, Nov 19 2008: (Start)

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

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

E.g.f.: (4/sqrt(3))*exp(x)*sinh(sqrt(3)*x). - G. C. Greubel, Oct 31 2016

MATHEMATICA

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}]

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 *)

CROSSREFS

Sequence in context: A159612 A099176 A190156 * A010366 A222356 A214201

Adjacent sequences:  A116553 A116554 A116555 * A116557 A116558 A116559

KEYWORD

nonn,easy,less

AUTHOR

Roger L. Bagula, Mar 15 2006

EXTENSIONS

Edited by N. J. A. Sloane, Dec 04 2006

STATUS

approved

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Last modified May 27 07:51 EDT 2017. Contains 287202 sequences.