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A224428
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The hyper-Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference.
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1
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1032, 54472, 853256, 8392840, 64852872, 433408392, 2632152456, 14947110280, 80788946312, 420521631112, 2125121035656, 10487138557320, 50753701289352, 241670439050632, 1135046330686856, 5268615489133960, 24208077521689992, 110246366797634952
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OFFSET
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0,1
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COMMENTS
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a(1) has been checked by the direct computation of the Wiener index (using Maple).
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REFERENCES
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A. R. Ashrafi and M. Mirzargar, The study of an infinite class of dendrimer nanostars by topological index approaches, J. Appl. Math. Comput, 31, 2009, 289-294.
M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).
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LINKS
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FORMULA
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a(n) = 7560 - 64000*4^n*n - 113312*2^n + 106784*4^n + 25600*4^n*n^2.
G.f.: 8*(129+4874*x+15616*x^2+4896*x^3)/((1-x)*(1-2*x)*(1-4*x)^3). [Bruno Berselli, Apr 06 2013]
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MAPLE
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a := proc (n) options operator, arrow: 7560-113312*2^n+25600*4^n*n^2-64000*4^n*n+106784*4^n end proc: seq(a(n), n = 0 .. 18);
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MATHEMATICA
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CoefficientList[Series[8 (129 + 4874 x + 15616 x^2 + 4896 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^3), {x, 0, 20}], x] (* Bruno Berselli, Apr 06 2013 *)
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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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