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%I #11 May 30 2018 10:27:59
%S 1248,136272,1590360,11608536,69325368,371933112,1870634040,
%T 9019095096,42224645688,193479671352,872186750520,3881641715256,
%U 17097660401208,74673784423992,323824724575800,1395810233321016,5985270160655928,25549161151039032,108628885484045880
%N The Wiener index of the polyphenylene dendrimer G[n] defined pictorially in the N. E. Arif et al. reference.
%C a(0) has been checked by the direct computation of the Wiener index (using Maple).
%H Colin Barker, <a href="/A224435/b224435.txt">Table of n, a(n) for n = 0..1000</a>
%H N. E. Arif, Roslan Hasni and Saeid Alikhani, <a href="http://dx.doi.org/10.3923/jas.2012.2279.2282">Fourth order and fourth sum connectivity indices of polyphenylene dendrimers</a>, J. Applied Science, 12 (21), 2012, 2279-2282.
%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) = -31176 + 136464*2^n + 93600*n*4^n - 31860*n*2^n - 104040*4^n.
%F G.f.: 24*(52 + 5002*x - 4221*x^2 - 22060*x^3 + 9536*x^4)/((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2).
%F a(n) = 13*a(n-1) - 64*a(n-2) + 148*a(n-3) - 160*a(n-4) + 64*a(n-5) for n>4.
%p a := proc (n) options operator, arrow: -31176+136464*2^n+93600*4^n*n-31860*2^n*n-104040*4^n end proc: seq(a(n), n = 0 .. 18);
%o (PARI) Vec(24*(52 + 5002*x - 4221*x^2 - 22060*x^3 + 9536*x^4) / ((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2) + O(x^50)) \\ _Colin Barker_, May 30 2018
%Y Cf. A224436.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Apr 06 2013
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