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%I #19 Jun 15 2018 05:51:02
%S 666,35325,412443,3099663,19013175,104225031,533102247,2604327399,
%T 12319287399,56913753447,258258898791,1155566158695,5112617020263,
%U 22412337970023,97497752214375,421386451835751,1811131262622567,7746874238425959
%N The Wiener index of the nanostar dendrimer D_n, defined pictorially in the Ghorbani et al. references and recursively in the Deutsch et al. reference.
%C a(1) has been checked by the direct computation of the Wiener index (using Maple).
%C In the Ghorbani & Songhori reference the formula for the Wiener index (p. 62) contains some errors.
%C The Deutsch et al. reference contains also the Hosoya polynomial of D_n.
%H Muniru A Asiru, <a href="/A227490/b227490.txt">Table of n, a(n) for n = 1..500</a>
%H E. Deutsch, S. Klavzar, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match70/n2/match70n2_627-644.pdf">Computing the Hosoya polynomial of graphs from primary subgraphs</a>, MATCH Commun. Math. Comput. Chem., 70, 2013, 627-644.
%H M. Ghorbani, A. Mohammadi, F. Madadi, <a href="https://oam-rc.inoe.ro/download.php?idu=1354">Some topological indices of nanostar dendrimers</a>, Optoelectronics and Adv. Materials - Rapid Comm., 4, 2010, 1871-1873.
%H M. Ghorbani and M. Songhori, <a href="http://dx.doi.org/10.22052/ijmc.2010.5155">Some topological indices of nanostar dendrimers</a>, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-42,64,-32).
%F a(n) = - 9369 + 56205*2^(n-1) - 75411*2^(2n-2) + 29241*2^(2n-2)*n.
%F G.f.: 9*x*(74 + 3111*x + 5760*x^2 + 424*x^3)/((1-x)*(1-2*x)*(1-4*x)^2).
%F a(n) = 11*a(n-1) - 42*a(n-2) + 64*a(n-3) - 32*a(n-4) for n>4. - _Colin Barker_, Jun 15 2018
%p a := proc (n) options operator, arrow: -9369+56205*2^(n-1)-75411*2^(2*n-2)+29241*2^(2*n-2)*n end proc: seq(a(n), n = 1 .. 22);
%t Table[-9369+56205*2^(n-1)-75411*2^(2n-2)+29241*2^(2n-2) n,{n,20}] (* or *) LinearRecurrence[{11,-42,64,-32},{666,35325,412443,3099663},20] (* _Harvey P. Dale_, Dec 24 2017 *)
%o (GAP) List([1..20], n-> 29241*2^(2*n-2)*n-75411*2^(2*n-2)+56205*2^(n-1)-9369); # _Muniru A Asiru_, Jun 15 2018
%o (PARI) Vec(9*x*(74 + 3111*x + 5760*x^2 + 424*x^3)/((1-x)*(1-2*x)*(1-4*x)^2) + O(x^40)) \\ _Colin Barker_, Jun 15 2018
%Y Cf. A227491.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Jul 16 2013