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A221012 The Wiener index of the nanostar dendrimer G_n , defined pictorially in the Golriz - Darafsheh - Khalifeh reference. 2
1248, 28184, 264576, 1799200, 10428288, 55146624, 275248896, 1321299200, 6169283328, 28218321664, 127045890816, 564885984000, 2486370202368, 10852804162304, 47040516846336, 202679222137600, 868785296241408, 3707414154572544, 15758746697331456, 66751342552544000, 281870782248776448 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Golriz, M. R. Darafsheh, and M. H. Khalifeh, The Wiener, Szeged and PI-indices of a phenylazomethine dendrimer, Digest J. Nanomaterials and Biostructures, 6, No. 4, 2011, 1545-1549.

FORMULA

a(n) = -3328 - 2^n*(1820*n-18616) +4^n*(13520*n-14040) - see Theorem 4 in the Golriz et al. reference; it has a typo: change 181616 to 18616.

G.f.: 104*(12+115*x-211*x^2-204*x^3)/((1-x)*(1-2*x)^2*(1-4*x)^2). - Bruno Berselli, Dec 30 2012

MAPLE

a := proc (n) options operator, arrow: -3328-2^n*(1820*n-18616)+4^n*(13520*n-14040) end proc: seq(a(n), n = 0 .. 20);

MATHEMATICA

CoefficientList[Series[104 *(12 + 115 * x - 211 * x^2 - 204 * x^3) / ((1 - x) * (1 - 2*x)^2 * (1 - 4*x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 30 2012 *)

CROSSREFS

Cf. A221013.

Sequence in context: A184500 A234212 A047629 * A233167 A266037 A233179

Adjacent sequences:  A221009 A221010 A221011 * A221013 A221014 A221015

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Dec 29 2012

STATUS

approved

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Last modified May 23 09:46 EDT 2022. Contains 353975 sequences. (Running on oeis4.)