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A224427 The Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference. 1

%I

%S 343,8967,88679,620839,3667623,19657127,99084199,479187879,2250222503,

%T 10338917287,46716074919,208322526119,919156226983,4020155841447,

%U 17454879996839,75316812315559,323256950193063,1380987667741607,5875792265345959

%N The Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference.

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

%D A. R. Ashrafi and M. Mirzargar, The study of an infinite class of dendrimer nanostars by topological index approaches, J. Appl. Math. Comput, 31, 2009, 289-294.

%D M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).

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

%F a(n) = -1113 + 8112*2^n - 6656*4^n + 5120*n*4^n.

%F G.f.: (343+5194*x+4448*x^2+32*x^3)/((1-x)*(1-2*x)*(1-4*x)^2). [_Bruno Berselli_, Apr 06 2013]

%p a := proc (n) options operator, arrow: -1113+8112*2^n+5120*4^n*n-6656*4^n end proc: seq(a(n), n = 0 .. 18);

%t CoefficientList[Series[(343 + 5194 x + 4448 x^2 + 32 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^2), {x, 0, 20}], x] (* _Bruno Berselli_, Apr 06 2013 *)

%Y Cf. A224428.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Apr 06 2013

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Last modified August 13 05:11 EDT 2022. Contains 356077 sequences. (Running on oeis4.)