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 A227700 The hyper-Wiener index of the nanostar dendrimer defined pictorially in the Ashrafi et al. reference. 1

%I #11 Apr 18 2020 00:03:01

%S 299671,1624639,9938719,60310495,352063711,1970086879,10608950239,

%T 55279894495,280190685151,1387684298719,6740446216159,32207067824095,

%U 151750499712991,706442679304159,3254507926208479,14856796917219295,67277314593931231,302489552025567199

%N The hyper-Wiener index of the nanostar dendrimer defined pictorially in the Ashrafi et al. reference.

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

%H A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match65/n1/match65n1_193-200.pdf">Computing Wiener and detour indices of a new type of nanostar dendrimers</a>, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200.

%F a(n) = 16351 + 2^n*(26400*n^2 + 52080*n + 40656) + 4^n*(57600*n^2 + 42240*n + 242664).

%F G.f.: (299671 - 4069110*x + 24021228*x^2 -75420072*x^3 + 131188512*x^4 -120811392*x^5 + 45232640*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

%p a := proc (n) options operator, arrow: 16351+2^n*(26400*n^2+52080*n+40656)+4^n*(57600*n^2+42240*n+242664) end proc: seq(a(n), n = 0 .. 22);

%t nn:=19; CoefficientList[Series[(299671 - 4069110*x + 24021228*x^2 -75420072*x^3 + 131188512*x^4 -120811392*x^5 + 45232640*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3), {x, 0, nn}], x] (* _Georg Fischer_, Apr 17 2020 *)

%Y Cf. A227699.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jul 21 2013

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Last modified April 16 10:24 EDT 2024. Contains 371700 sequences. (Running on oeis4.)