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A224424 The hyper-Wiener index of the Micelle-like chiral dendrimer G[n] defined pictorially in the Hassan Yousefi-Azari et al. reference. 1
147859, 984643, 6530659, 40951843, 241838755, 1355802019, 7283759011, 37802644387, 190766807971, 940772076451, 4551624543139, 21670926257059, 101780972047267, 472467096865699, 2171047575817123, 9888107533437859, 44684841214544803 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(0) has been checked by the direct computation of the Wiener index (using Maple).

LINKS

Table of n, a(n) for n=0..16.

H. Yousefi-Azari, A. R. Ashrafi, and M. H. Khalifeh, Wiener index of micelle-like chiral dendrimers, Studia UBB, Chemia, 55, No. 4, 125-130, 2010.

Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).

FORMULA

a(n) = 2979 + 13680*2^n + 131200*4^n + 52224*n*4^n + 30240*n*2^n + 36864*n^2*4^n + 6336*n^2*2^n.

a(n) = 19*a(n-1)-150*a(n-2)+636*a(n-3)-1560*a(n-4)+2208*a(n-5)-1664*a(n-6)+512*a(n-7). [Bruno Berselli, Apr 06 2013]

G.f.: -(13735424*x^6 -40286592*x^5 +47779680*x^4 -29472552*x^3 +10001292*x^2 -1824678*x +147859) / ((x-1)*(2*x-1)^3*(4*x-1)^3). [Colin Barker, Apr 15 2013]

MAPLE

a := proc (n) options operator, arrow: 2979 + 36864*4^n*n^2 + 13680*2^n + 30240*2^n*n + 52224*4^n*n + 6336*2^n*n^2 + 131200*4^n end proc: seq(a(n), n = 0 .. 15);

MATHEMATICA

a = {147859, 984643, 6530659, 40951843, 241838755, 1355802019, 7283759011}; Do[AppendTo[a, 19 a[[-1]] - 150 a[[-2]] + 636 a[[-3]] - 1560 a[[-4]] + 2208 a[[-5]] - 1664 a[[-6]] + 512 a[[-7]]], {10}]; a (* Bruno Berselli, Apr 06 2013 *)

PROG

(MAGMA) [2979+13680*2^n+131200*4^n+52224*n*4^n+30240*n*2^n+ 36864*n^2*4^n+6336*n^2*2^n: n in [0..25]]; // Vincenzo Librandi, Nov 13 2016

CROSSREFS

Cf. A224423.

Sequence in context: A204105 A015317 A195363 * A065323 A252909 A254088

Adjacent sequences:  A224421 A224422 A224423 * A224425 A224426 A224427

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Apr 06 2013

STATUS

approved

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Last modified August 17 21:56 EDT 2022. Contains 356189 sequences. (Running on oeis4.)