login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109112 a(n) = 6*a(n-1) - 3*a(n-2), a(0)=2, a(1)=13. 0
2, 13, 72, 393, 2142, 11673, 63612, 346653, 1889082, 10294533, 56099952, 305716113, 1665996822, 9078832593, 49475005092, 269613532773, 1469256181362, 8006696489853, 43632410395032, 237774372900633, 1295749006218702 (list; graph; refs; listen; history; text; internal format)
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).

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

AUTHOR

Emeric Deutsch, Jun 19 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 03:12 EDT 2020. Contains 334828 sequences. (Running on oeis4.)