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The Wiener index of the Micelle-like chiral dendrimer G[n] defined pictorially in the Hassan Yousefi-Azari et al. reference.
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%I #15 Nov 13 2016 16:53:07

%S 24485,120741,613541,3078309,15070373,71955621,336069797,1540900005,

%T 6958417061,31031755941,136961328293,599275078821,2603021763749,

%U 11236212212901,48242297406629,206161018094757,877415731561637,3720758807233701,15727438348682405

%N The Wiener index of the Micelle-like chiral dendrimer G[n] defined pictorially in the Hassan Yousefi-Azari et al. reference.

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

%H H. Yousefi-Azari, A. R. Ashrafi, and M. H. Khalifeh, <a href="http://studia.ubbcluj.ro/download/pdf/581.pdf">Wiener index of micelle-like chiral dendrimers</a>, Studia UBB, Chemia, 55, No. 4, 125-130, 2010.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,-64,148,-160,64).

%F a(n) = 1189 + 15616*2^n + 7680*4^n + 12288*n*4^n + 4224*n*2^n (agrees with Theorem 2 of the Yousefi-Azari et al. reference).

%F G.f.: (24485-197564*x+610948*x^2-794080*x^3+366912*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2). [_Bruno Berselli_, Apr 06 2013]

%p a := proc (n) options operator, arrow: 1189 + 15616*2^n + 4224*2^n*n + 12288*4^n*n + 7680*4^n end proc: seq(a(n), n = 0 .. 18);

%t CoefficientList[Series[(24485 - 197564 x + 610948 x^2 - 794080 x^3 + 366912 x^4)/((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 20}], x] (* _Bruno Berselli_, Apr 06 2013 *)

%Y Cf. A224424.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Apr 06 2013