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A216110
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The Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
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3
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27, 198, 621, 1404, 2655, 4482, 6993, 10296, 14499, 19710, 26037, 33588, 42471, 52794, 64665, 78192, 93483, 110646, 129789, 151020, 174447, 200178, 228321, 258984, 292275, 328302, 367173, 408996, 453879, 501930
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OFFSET
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1,1
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COMMENTS
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The Hosoya-Wiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{3n+1}-nt^4+nt-t)/(t^3-1)^2.
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REFERENCES
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Y. Dou, H. Bian, H. Gao, and H. Yu, The polyphenyl chains with extremal edge-Wiener indices, MATCH Commun. Math. Comput. Chem., 64, 2010, 757-766.
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LINKS
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FORMULA
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a(n) = 18n^3 + 18n^2 -9n.
G.f.: -9*x*(x^2-10*x-3)/(x-1)^4. [Colin Barker, Oct 30 2012]
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EXAMPLE
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a(1)=27 because the graph consists of 1 hexagon and the Wiener index is 6*1+6*2+3*3=27.
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MAPLE
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seq(18*n^3+18*n^2-9*n, n=1..30);
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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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