A109112 a(n) = 6*a(n-1) - 3*a(n-2), a(0)=2, a(1)=13.

2, 13, 72, 393, 2142, 11673, 63612, 346653, 1889082, 10294533, 56099952, 305716113, 1665996822, 9078832593, 49475005092, 269613532773, 1469256181362, 8006696489853, 43632410395032, 237774372900633, 1295749006218702

Offset

0,1

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_{14}).

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (6,-3).

Formula

a(n) = (1/(2*sqrt(6)))*((2*sqrt(6) + 7)*(3 + sqrt(6))^n + (2*sqrt(6) - 7)*(3 - sqrt(6))^n).

G.f.: (2+z)/(1 - 6z + 3z^2).

a(n) = 2*A138395(n) + A138395(n-1). - R. J. Mathar, Jul 22 2022

Maple

a[0]:=2:a[1]:=13: for n from 2 to 24 do a[n]:=6*a[n-1]-3*a[n-2] od: seq(a[n], n=0..24);

Mathematica

LinearRecurrence[{6, -3}, {2, 13}, 30] (* Harvey P. Dale, Dec 15 2014 *)

Crossrefs

Sequence in context: A330499 A097349 A289790 * A163190 A242991 A240549

Adjacent sequences: A109109 A109110 A109111 * A109113 A109114 A109115

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 19 2005

Status

approved