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The Wiener index of the nanostar dendrimer G[n], defined pictorially in the Nadjafi-Arani et al. reference.
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%I #13 Feb 13 2024 08:15:42

%S 84,2328,23070,161322,951906,5097426,25678002,124125810,582682098,

%T 2676493554,12091136754,53909403378,237825453810,1040070008562,

%U 4515386474226,19482038992626,83610263027442,357169749688050,1519594327768818,6442039704551154

%N The Wiener index of the nanostar dendrimer G[n], defined pictorially in the Nadjafi-Arani et al. reference.

%C a(2) has been checked by the direct computation of the Wiener index (using Maple).

%C The formula on p. 163 of the Nadjafi-Arani reference seems to be mistaken.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-42,64,-32).

%H M. J. Nadjafi-Arani, H. Khodashenas, and A. R. Ashrafi, <a href="https://match.pmf.kg.ac.rs/electronic_versions/Match69/n1/match69n1_159-164.pdf">A new method for computing Wiener index of dendrimer nanostars</a>, MATCH Commun. Math. Comput. Chem. 69, 2013, 159-164.

%F a(n) = -270 + 2^(n-1)*2055+4^(n-1)*(1323*n-3024).

%F G.f.: -6*x*(-14-234*x-165*x^2+8*x^3) / ( (2*x-1)*(x-1)*(-1+4*x)^2 ). - _R. J. Mathar_, Apr 11 2013

%p a := proc (n) options operator, arrow: -270+2055*2^(n-1)+4^(n-1)*(1323*n-3024) end proc: seq(a(n), n = 1 .. 20);

%Y Cf. A221011.

%K nonn

%O 1,1

%A _Emeric Deutsch_, Mar 28 2013