A109113 a(n) = 6*a(n-1) + 3*a(n-2), a(0)=2, a(1)=14.

2, 14, 90, 582, 3762, 24318, 157194, 1016118, 6568290, 42458094, 274453434, 1774094886, 11467929618, 74129862366, 479182963050, 3097487365398, 20022473081538, 129427300585422, 836631222757146, 5408069238299142

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_{15}).

Links

Table of n, a(n) for n=0..19.

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

Formula

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

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

a(n) = 2*abs(A099842(n)). - F. Chapoton, May 06 2014

Maple

a[0]:=2: a[1]:=14: for n from 2 to 25 do a[n]:=6*a[n-1]+3*a[n-2] od: seq(a[n], n=0..22);

Mathematica

CoefficientList[Series[2*(1 + x)/(1 - 6*x - 3*x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jan 01 2024 *)

Prog

(PARI) Vec((14+6*x)/(1-6*x-3*x^2)+O(x^99)) \\ Charles R Greathouse IV, May 06 2014

Crossrefs

Cf. A099842.

Sequence in context: A065892 A139183 A174705 * A081959 A002464 A282051

Adjacent sequences: A109110 A109111 A109112 * A109114 A109115 A109116

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 19 2005

Status

approved