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

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

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

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

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: A099176 A190156 A291024 * A334324 A010366 A222356

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