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A228606
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The Merrifield-Simmons index of the para-polyphenylene chain of length n.
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2
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1, 18, 299, 4957, 82176, 1362293, 22583749, 374387682, 6206504351, 102889860193, 1705682092824, 28276366556657, 468758456813401, 7770959199931218, 128824997201136899, 2135628238019808757, 35403905065928790576, 586916988454650778493, 9729761468267561700349, 161297526041365993456482
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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) = ((19+3*sqrt(29))*(17+3*sqrt(29))^n - (19-3*sqrt(29))*(17-3*sqrt(29))^n)/(6*2^n*sqrt(29)).
G.f.: (1+x)/(1-17*x+7*x^2).
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MAPLE
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gser := series((x+1)/(7*x^2-17*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);
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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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