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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 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

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