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A109105
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a(n) = (8*sqrt(5)/25)((sqrt(5) + 2)((15 + 5*sqrt(5))/2)^n + (sqrt(5) - 2)((15 - 5*sqrt(5))/2)^n).
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0
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40, 520, 6800, 89000, 1165000, 15250000, 199625000, 2613125000, 34206250000, 447765625000, 5861328125000, 76725781250000, 1004353515625000, 13147158203125000, 172098535156250000, 2252799072265625000
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OFFSET
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1,1
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COMMENTS
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Kekulé numbers for certain benzenoids.
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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. 215, K{S_m}).
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LINKS
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FORMULA
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G.f.: 40*z(1-2*z)/(1 - 15*z + 25*z^2).
Let b(n) = 5^n*A001906(n+1) = 1, 15, 200, 2625,... (n>=0) then a(n) = 40*[b(n)-2*b(n-1)]. - R. J. Mathar, Jul 22 2022
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MAPLE
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a:=n->(8/5/sqrt(5))*((sqrt(5)+2)*((15+5*sqrt(5))/2)^n+(sqrt(5)-2)*((15-5*sqrt(5))/2)^n): seq(expand(a(n)), n=1..19);
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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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