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A224456
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The Wiener index of the cyclic phenylene with n hexagons (n>=3).
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1
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459, 1008, 1845, 3024, 4599, 6624, 9153, 12240, 15939, 20304, 25389, 31248, 37935, 45504, 54009, 63504, 74043, 85680, 98469, 112464, 127719, 144288, 162225, 181584, 202419, 224784, 248733, 274320, 301599, 330624, 361449, 394128, 428715, 465264, 503829, 544464, 587223, 632160
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OFFSET
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3,1
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COMMENTS
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a(3), a(4), ... , a(16) have been checked by the direct computation of the Wiener index (using Maple).
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REFERENCES
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Y. Alizadeh, S. Klavzar, The Wiener dimension of a graph (unpublished manuscript).
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LINKS
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FORMULA
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a(n) = 9n(n^2+4n-4).
G.f.: 9z^3(51-92z+63z^2-16z^3)/(1-z)^4.
The Hosoya polynomial of the cyclic phenylene with n hexagons is [n*t^n*(t^5+3t^4+5t^3+5t^2+3t+1) - n(t^8+t^7+t^6+t^5+2t^3+4t^2+8t)]/(t-1).
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MAPLE
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a := proc (n) options operator, arrow: 9*n*(n^2+4*n-4) end proc: seq(a(n), n = 3 .. 40);
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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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