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A224428
The hyper-Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference.
1
1032, 54472, 853256, 8392840, 64852872, 433408392, 2632152456, 14947110280, 80788946312, 420521631112, 2125121035656, 10487138557320, 50753701289352, 241670439050632, 1135046330686856, 5268615489133960, 24208077521689992, 110246366797634952
OFFSET
0,1
COMMENTS
a(1) has been checked by the direct computation of the Wiener index (using Maple).
REFERENCES
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M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).
FORMULA
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]
MAPLE
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);
MATHEMATICA
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 *)
CROSSREFS
Cf. A224427.
Sequence in context: A023062 A035046 A282357 * A283724 A168225 A282576
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 06 2013
STATUS
approved