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A224425 The Wiener index of the phenylacetylene dendrimer NSB[n], defined pictorially in the Z. Yarahmadi et al. reference. 1
10584, 171477, 1461051, 9546255, 54280503, 284162823, 1410216615, 6746016231, 31426525287, 143519749479, 645421289319, 2867229803367, 12611448843111, 55016616065895, 238351151471463, 1026546163669863, 4398756503804775, 18765324647783271, 79742515593599847 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(0) has been checked by the direct computation of the Wiener index (using Maple).

LINKS

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

Z. Yarahmadi, Eccentric connectivity and augmented eccentric connectivity indices of N-branches phenylacetylenes nanostar dendrimers, Iranian J. Math. Chem., 1, No. 2, 2010, 105-110.

Z. Yarahmadi and G. H. Fath-Tabar, The Wiener, Szeged, PI, Vertex PI, the first and second Zagreb indices of N-branched phenylacetylenes dendrimers,  MATCH: Commun. Math. Comput. Chem, 65 (2011)  201-208.

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

FORMULA

a(n) = -9369 + 85725*2^n - 65772*4^n +68121*n*4^n  (agrees with Theorem 3 of the Yarahmadi et al. reference).

G.f.: 27*(392+2039*x+716*x^2-24*x^3)/((1-x)*(1-2*x)*(1-4*x)^2). [Bruno Berselli, Apr 06 2013]

MAPLE

a := proc (n) options operator, arrow: -9369+68121*4^n*n+85725*2^n-65772*4^n end proc: seq(a(n), n = 0 .. 18);

MATHEMATICA

CoefficientList[Series[27 (392 + 2039 x + 716 x^2 - 24 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^2), {x, 0, 20}], x] (* Bruno Berselli, Apr 06 2013 *)

CROSSREFS

Cf. A224426.

Sequence in context: A063433 A089494 A066054 * A179426 A229881 A070249

Adjacent sequences:  A224422 A224423 A224424 * A224426 A224427 A224428

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Apr 06 2013

STATUS

approved

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Last modified August 13 05:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)