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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
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).
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