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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 (list; graph; refs; listen; history; text; internal format)
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M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).

LINKS

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (11,-42,64,-32).

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

Adjacent sequences:  A224424 A224425 A224426 * A224428 A224429 A224430

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Apr 06 2013

STATUS

approved

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Last modified June 24 21:51 EDT 2022. Contains 354830 sequences. (Running on oeis4.)