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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A109114 a(n) = 5*a(n-1) - 3*a(n-2), a(0)=1, a(1)=6. 3
 1, 6, 27, 117, 504, 2169, 9333, 40158, 172791, 743481, 3199032, 13764717, 59226489, 254838294, 1096512003, 4718045133, 20300689656, 87349312881, 375844495437, 1617174538542, 6958339206399, 29940172416369, 128825844462648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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_{11}). LINKS Index entries for linear recurrences with constant coefficients, signature (5,-3). FORMULA a(n) = ((sqrt(13) + 7)*((5 + sqrt(13))/2)^n + (sqrt(13) - 7)*((5 - sqrt(13))/2)^n)/(2*sqrt(13)). G.f.: (1+z)/(1 - 5z + 3z^2). MAPLE a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=5*a[n-1]-3*a[n-2] od: seq(a[n], n=0..26); MATHEMATICA LinearRecurrence[{5, -3}, {1, 6}, 30] (* Harvey P. Dale, Dec 03 2012 *) CROSSREFS Sequence in context: A130019 A196919 A049651 * A080619 A265943 A080620 Adjacent sequences:  A109111 A109112 A109113 * A109115 A109116 A109117 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.

Last modified May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)