A109115 a(n) = 4*a(n-1) + 3*a(n-2), a(0)=1, a(1)=6.

1, 6, 27, 126, 585, 2718, 12627, 58662, 272529, 1266102, 5881995, 27326286, 126951129, 589783374, 2739986883, 12729297654, 59137151265, 274736498022, 1276357445883, 5929639277598, 27547629448041, 127979435624958

Offset

0,2

Comments

Kekulé numbers for certain benzenoids.

References

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 302, P_{12}).

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (4, 3).

Formula

a(n) = ((sqrt(7) + 4)*(2 + sqrt(7))^n + (sqrt(7) - 4)*(2 - sqrt(7))^n)/(2*sqrt(7)).

G.f.: (1+2z)/(1 - 4z - 3z^2).

a(n) = A015530(n+1)+2*A015530(n). - R. J. Mathar, Jul 26 2022

Maple

a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=4*a[n-1]+3*a[n-2] od: seq(a[n], n=0..26);

Mathematica

LinearRecurrence[{4, 3}, {1, 6}, 40] (* Harvey P. Dale, Aug 20 2020 *)

Crossrefs

Sequence in context: A030297 A045500 A360057 * A038176 A104745 A184279

Adjacent sequences: A109112 A109113 A109114 * A109116 A109117 A109118

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 19 2005

Status

approved