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

Author

Emeric Deutsch, Jun 19 2005

Keywords

• nonn
• easy

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

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

Programs

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 *)

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