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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
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}).
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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved