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A107971
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a(n) = (n+1)(n+2)(n+3)(35n^3 + 153n^2 + 232n + 120)/720.
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0
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1, 18, 123, 523, 1673, 4424, 10206, 21246, 40821, 73546, 125697, 205569, 323869, 494144, 733244, 1061820, 1504857, 2092242, 2859367, 3847767, 5105793, 6689320, 8662490, 11098490, 14080365, 17701866, 22068333, 27297613, 33521013, 40884288
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OFFSET
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0,2
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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. 230).
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LINKS
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FORMULA
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O.g.f.: -(1 + 11x + 18x^2 + 5x^3)/(-1+x)^7.
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MAPLE
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a:=n->(1/720)*(n+1)*(n+2)*(n+3)*(35*n^3+153*n^2+232*n+120): seq(a(n), n=0..35);
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MATHEMATICA
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Table[(n+1)(n+2)(n+3)(35n^3+153n^2+232n+120)/720, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 18, 123, 523, 1673, 4424, 10206}, 30] (* Harvey P. Dale, Jan 05 2022 *)
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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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