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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
OFFSET
0,2
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_{11}).
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).
a(n) = A116415(n)+A116415(n-1). - R. J. Mathar, Jul 26 2022
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 * A373302 A080619 A265943
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved