A221005 The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Wang-Hua reference.

4797, 18800, 88530, 500582, 3112014, 19362974, 115754814, 659875454, 3602117886, 18956429822, 96789115902, 482029987838, 2351490682878, 11274381991934, 53269435990014, 248554431348734, 1147271095058430, 5245861041405950, 23788748016975870, 107088865925791742, 478941290597187582

Offset

0,1

Links

Table of n, a(n) for n=0..20.

H. Wang and H. Hua, Computing the second- and third- connectivity index of an infinite class of dendrimer nanostars, Digest J. Nanomaterials and Biostructures, 5 (2010) 497-502.

L. Yang and H. Hua, Modified terminal Wiener index of a type of dendrimer nanostars, Optoelectronics and Advanced Materials - Rapid Communications, 5 (2011) 160-163.

Formula

a(n) = -2+2^n*(1404*n^2+1764*n-3115)+4^n*(1296*n^2-4536*n+7914).

G.f.: (4797-72343*x+450880*x^2-1412380*x^3+2406976*x^4-2246848*x^5+868864*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3). - Bruno Berselli, Dec 30 2012

Maple

a := proc (n) options operator, arrow: -2+2^n*(1404*n^2+1764*n-3115)+4^n*(1296*n^2-4536*n+7914) end proc: seq(a(n), n = 0 .. 20);

Crossrefs

Cf. A221004.

Sequence in context: A296812 A251775 A096517 * A227495 A254035 A255412

Adjacent sequences: A221002 A221003 A221004 * A221006 A221007 A221008

Keyword

nonn,easy

Author

Emeric Deutsch, Dec 29 2012

Status

approved