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%I #21 Nov 17 2016 03:02:52
%S 68556,2138994,27959412,251530740,1844957748,11922051060,70741011828,
%T 394986935412,2107840963188,10863256632948,54464106804852,
%U 267039247214196,1285451192174196,6093251133916788,28507903924684404,131887740411168372,604241712010610292
%N The hyper-Wiener index of the phenylacetylene dendrimer NSB[n], defined pictorially in the Z. Yarahmadi et al. reference.
%C a(0) has been checked by the direct computation of the Wiener index (using Maple).
%H Vincenzo Librandi, <a href="/A224426/b224426.txt">Table of n, a(n) for n = 0..200</a>
%H Z. Yarahmadi, <a href="http://dx.doi.org/10.22052/ijmc.2010.5154">Eccentric connectivity and augmented eccentric connectivity indices of N-branches phenylacetylenes nanostar dendrimers</a>, Iranian J. Math. Chem., 1, No. 2, 2010, 105-110.
%H Z. Yarahmadi and G. H. Fath-Tabar, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match65/n1/match65n1_201-208.pdf">The Wiener, Szeged, PI, Vertex PI, the first and second Zagreb indices of N-branched phenylacetylenes dendrimers</a>, MATCH: Commun. Math. Comput. Chem, 65 (2011) 201-208.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-86,232,-288,128)
%F a(n) = 116340 - 2180388*2^n + 2132604*4^n - 2299671*4^n*n/2 + 613089*4^n*n^2.
%F G.f.: 6*(11426+185109*x+295053*x^2+31342*x^3+600*x^4)/((1-x)*(1-2*x)*(1-4*x)^3).
%p 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);
%t 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 *)
%Y Cf. A224425.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Apr 06 2013
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