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A227700 The hyper-Wiener index of the nanostar dendrimer defined pictorially in the Ashrafi et al. reference. 1
299671, 1624639, 9938719, 60310495, 352063711, 1970086879, 10608950239, 55279894495, 280190685151, 1387684298719, 6740446216159, 32207067824095, 151750499712991, 706442679304159, 3254507926208479, 14856796917219295, 67277314593931231, 302489552025567199 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(1) has been checked by the direct computation of the Wiener index (using Maple).
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 21 2013
STATUS
approved

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Last modified March 1 13:16 EST 2024. Contains 370433 sequences. (Running on oeis4.)