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A228604
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The Merrifield-Simmons index of the ortho-polyphenylene chain of length n.
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2
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1, 18, 299, 4932, 81301, 1340118, 22089599, 364109832, 6001737001, 98928520218, 1630669938899, 26878845894732, 443052477632701, 7302973450020318, 120377210159548199, 1984215446621359632, 32706447785195768401, 539110673967989840418, 8886330936793922917499
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OFFSET
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0,2
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COMMENTS
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The Merrifield-Simmons index of a graph is the number of its independent vertex subsets.
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REFERENCES
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R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989.
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LINKS
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FORMULA
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a(n) = ((9 + 2*sqrt(14))^(n+1) - (9 - 2*sqrt(14))^(n+1))/(4*sqrt(14)).
G.f. = 1/(1 - 18*x + 25*x^2).
a(n) = 18*a(n-1) - 25*a(n-2); a(0)=1, a(1)=18. - Harvey P. Dale, Nov 06 2014
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MAPLE
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gser := series(1/(25*x^2-18*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);
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MATHEMATICA
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CoefficientList[Series[1/(1-18x+25x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[ {18, -25}, {1, 18}, 20] (* Harvey P. Dale, Nov 06 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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