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A109113
a(n) = 6*a(n-1) + 3*a(n-2), 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
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}).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved