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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 (list; graph; refs; listen; history; text; internal format)
 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_{14}). LINKS 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

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