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A224430 The hyper-Wiener index of the dendrimer D_1[n], defined pictorially in the A. R. Ashrafi et al. reference. 1
159, 104448, 2123802, 22761810, 183445458, 1256801106, 7758199698, 44564150802, 242917046802, 1272665857554, 6464520301074, 32033885569554, 155562155893266, 742852590887442, 3497424488243730, 16268164668891666, 74884202558956050, 341573770043761170, 1545606217427624466 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(2) has been checked by the direct computation of the hyper-Wiener index (using Maple).

REFERENCES

A. R. Ashrafi and H. Shabani, Computing Padmakar-Ivan index of four classes of dendrimers, Bulgarian Chem. Comm., 44, N0. 2, 2012, 127-130.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = 41490 - 420000*2^n + 81225*4^n*n^2 - 467115*4^n*n/2 + 378669*4^n + 231*2^n*n - 1425*2^n*n^2.

G.f. = 3(53+33809z+54380z^2-674784z^3+1120160z^4-847120z^5+686912z^6)/[(1-z)(1-2z)^3*(1-4z)^3].

MAPLE

a := proc (n) options operator, arrow: 41490-420000*2^n+81225*4^n*n^2-(467115/2)*4^n*n+378669*4^n+231*2^n*n-1425*2^n*n^2 end proc: seq(a(n), n = 0 .. 18);

CROSSREFS

Cf. A224429

Sequence in context: A268029 A263518 A213695 * A013454 A013455 A013465

Adjacent sequences:  A224427 A224428 A224429 * A224431 A224432 A224433

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 06 2013

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)