A224425 The Wiener index of the phenylacetylene dendrimer NSB[n], defined pictorially in the Z. Yarahmadi et al. reference.

10584, 171477, 1461051, 9546255, 54280503, 284162823, 1410216615, 6746016231, 31426525287, 143519749479, 645421289319, 2867229803367, 12611448843111, 55016616065895, 238351151471463, 1026546163669863, 4398756503804775, 18765324647783271, 79742515593599847

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