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A227711
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The hyper-Wiener index of the nanostar dendrimer defined pictorially in Fig. 2 of the Madanshekaf reference.
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2
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403929, 7123491, 73556943, 584118615, 3973793223, 24439248231, 140086159911, 762624306855, 3992164666791, 20266876319655, 100389136655271, 487362872044455, 2326764524198823, 10952675858742183, 50938660677696423, 234448450914335655, 1069296992883227559
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OFFSET
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1,1
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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. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, 2011, 1075-1080.
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LINKS
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FORMULA
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a(n) = 4^n*(254016*n^2-728028*n+1207116) + 2^n*(13104*n^2-50682*n-1250685)+48039.
G.f.: 3*x*(134643-183720*x-400012*x^2-612832*x^3+2889984*x^4 -2158592*x^5 +762880*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).
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MAPLE
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a := proc (n) options operator, arrow: 4^n*(254016*n^2-728028*n+1207116) +2^n*(13104*n^2-50682*n-1250685)+48039 end proc: seq(a(n), n = 1 .. 20);
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MATHEMATICA
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CoefficientList[Series[3 (134643 - 183720 x - 400012 x^2 - 612832 x^3 + 2889984 x^4 - 2158592 x^5 + 762880 x^6) / ((1 - x) (1 - 2 x)^3 (1 - 4 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
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PROG
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(Magma) [4^n*(254016*n^2-728028*n+1207116)+2^n*(13104*n^2-50682*n-1250685)+48039: n in [1..20]]; // Vincenzo Librandi, Aug 04 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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EXTENSIONS
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STATUS
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approved
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