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A224426 The hyper-Wiener index of the phenylacetylene dendrimer NSB[n], defined pictorially in the Z. Yarahmadi et al. reference. 2
68556, 2138994, 27959412, 251530740, 1844957748, 11922051060, 70741011828, 394986935412, 2107840963188, 10863256632948, 54464106804852, 267039247214196, 1285451192174196, 6093251133916788, 28507903924684404, 131887740411168372, 604241712010610292 (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

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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 (15,-86,232,-288,128)

FORMULA

a(n) = 116340 - 2180388*2^n + 2132604*4^n - 2299671*4^n*n/2 + 613089*4^n*n^2.

G.f.: 6*(11426+185109*x+295053*x^2+31342*x^3+600*x^4)/((1-x)*(1-2*x)*(1-4*x)^3).

MAPLE

a := proc (n) options operator, arrow: 116340-(2299671/2)*4^n*n-2180388*2^n+2132604*4^n+613089*4^n*n^2 end proc: seq(a(n), n = 0 .. 16);

MATHEMATICA

CoefficientList[Series[6 (11426 + 185109 x + 295053 x^2 + 31342 x^3 + 600 x^4) / ((1 - x) (1 - 2 x) (1 - 4 x)^3), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 26 2013 *)

CROSSREFS

Cf. A224425.

Sequence in context: A205203 A205061 A093217 * A031845 A249315 A031863

Adjacent sequences:  A224423 A224424 A224425 * A224427 A224428 A224429

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Apr 06 2013

STATUS

approved

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Last modified August 9 16:21 EDT 2022. Contains 356026 sequences. (Running on oeis4.)