A227492 - OEIS

%I #17 May 27 2018 07:08:52

%S 27,2871,39663,326367,2123199,12126591,63900927,319163391,1535375871,

%T 7186396671,32947236351,148643831295,662099705343,2918722534911,

%U 12756670414335,55354839662079,238734196604415,1024200814362111,4373869249953279

%N The Wiener index of the nanostar dendrimer D_n.

%C D_n is defined pictorially as NS2[n] in the Chen et al. reference.

%C a(1) and a(2) have been checked by the direct computation of the Wiener index (using Maple).

%H S. Chen and J. Yang, <a href="http://www.m-hikari.com/imf-2011/5-8-2011/chenshuboIMF5-8-2011.pdf">Second-order and third-order connectivity indices of dendrimer nanostars</a>, International Mathematical Forum, 6, No, 5, 2011, 223-228.

%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) = - 513 + 2^n*(2016*n + 9468) + 4^n*(4032*n - 8928).

%F G.f.: 9*(3 + 280*x + 452*x^2 - 1056*x^3 - 192*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2).

%p a := proc (n) options operator, arrow: -513+2^n*(2016*n+9468)+4^n*(4032*n-8928) end proc: seq(a(n), n = 0 .. 20);

%t LinearRecurrence[{13,-64,148,-160,64},{27,2871,39663,326367,2123199},20] (* _Harvey P. Dale_, Dec 30 2017 *)

%Y Cf. A227493.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jul 17 2013