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A114481 Kekulé numbers for certain benzenoids. 0
5, 105, 2331, 52137, 1167291, 26137809, 585284211, 13105857753, 293470347915, 6571477451169, 147150526244067, 3295039441438377, 73783527649203195, 1652183243687500785, 36996190853123920851, 828429983702209723257 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 205).
LINKS
FORMULA
a(n) = (3^(n+1) + (12 + 6*sqrt(3))^(n+1)/4 + (12 - 6*sqrt(3))^(n+1)/4)/27.
From Colin Barker, Aug 30 2013: (Start)
a(n) = 27*a(n-1) - 108*a(n-2) + 108*a(n-3).
G.f.: -x*(36*x^2 - 30*x + 5) / ((3*x-1)*(36*x^2 - 24*x + 1)). (End)
9*a(n) = 3^n+ 6^n*A001075(n+1). - R. J. Mathar, Jul 22 2022
MAPLE
a:=n->(3^(n+1)+(12+6*sqrt(3))^(n+1)/4+(12-6*sqrt(3))^(n+1)/4)/27: seq(expand(a(n)), n=1..18);
CROSSREFS
Sequence in context: A327273 A034225 A273966 * A273962 A223043 A200851
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 30 2005
STATUS
approved

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Last modified April 24 07:54 EDT 2024. Contains 371922 sequences. (Running on oeis4.)