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A224427
The Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference.
1
343, 8967, 88679, 620839, 3667623, 19657127, 99084199, 479187879, 2250222503, 10338917287, 46716074919, 208322526119, 919156226983, 4020155841447, 17454879996839, 75316812315559, 323256950193063, 1380987667741607, 5875792265345959
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M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).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) = -1113 + 8112*2^n - 6656*4^n + 5120*n*4^n.
G.f.: (343+5194*x+4448*x^2+32*x^3)/((1-x)*(1-2*x)*(1-4*x)^2). [Bruno Berselli, Apr 06 2013]
MAPLE
a := proc (n) options operator, arrow: -1113+8112*2^n+5120*4^n*n-6656*4^n end proc: seq(a(n), n = 0 .. 18);
MATHEMATICA
CoefficientList[Series[(343 + 5194 x + 4448 x^2 + 32 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^2), {x, 0, 20}], x] (* Bruno Berselli, Apr 06 2013 *)
CROSSREFS
Cf. A224428.
Sequence in context: A017475 A017607 A277636 * A134263 A270820 A140250
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 06 2013
STATUS
approved