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

299671, 1624639, 9938719, 60310495, 352063711, 1970086879, 10608950239, 55279894495, 280190685151, 1387684298719, 6740446216159, 32207067824095, 151750499712991, 706442679304159, 3254507926208479, 14856796917219295, 67277314593931231, 302489552025567199

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..17.

A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, Computing Wiener and detour indices of a new type of nanostar dendrimers, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200.

Formula

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

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).

Maple

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);

Mathematica

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 *)

Crossrefs

Cf. A227699.

Sequence in context: A254186 A253798 A022246 * A050257 A283209 A113939

Adjacent sequences: A227697 A227698 A227699 * A227701 A227702 A227703

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 21 2013

Status

approved