

A109113


a(n) = 6a(n1) + 3a(n2), a(0)=2, a(1)=14.


0



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

0,1


COMMENTS

KekulĂ© numbers for certain benzenoids.


REFERENCES

S. J. Cyvin and I. Gutman, KekulĂ© 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 + 2sqrt(3))^(n+1) + (3  2sqrt(3))^(n+1))/3.
G.f.: 2(1+z)/(1  6z  3z^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[n1]+3*a[n2] od: seq(a[n], n=0..22);


PROG

(PARI) Vec((14+6*x)/(16*x3*x^2)+O(x^99)) \\ Charles R Greathouse IV, May 06 2014


CROSSREFS

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



