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A114481
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Kekulé numbers for certain benzenoids.
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0
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5, 105, 2331, 52137, 1167291, 26137809, 585284211, 13105857753, 293470347915, 6571477451169, 147150526244067, 3295039441438377, 73783527649203195, 1652183243687500785, 36996190853123920851, 828429983702209723257
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OFFSET
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1,1
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 205).
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LINKS
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FORMULA
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a(n) = (3^(n+1) + (12 + 6*sqrt(3))^(n+1)/4 + (12 - 6*sqrt(3))^(n+1)/4)/27.
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)
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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