A221010 The Wiener index of the nanostar dendrimer G[n], defined pictorially in the Nadjafi-Arani et al. reference.

84, 2328, 23070, 161322, 951906, 5097426, 25678002, 124125810, 582682098, 2676493554, 12091136754, 53909403378, 237825453810, 1040070008562, 4515386474226, 19482038992626, 83610263027442, 357169749688050, 1519594327768818, 6442039704551154

Offset

1,1

Comments

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

The formula on p. 163 of the Nadjafi-Arani reference seems to be mistaken.

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (11,-42,64,-32).

M. J. Nadjafi-Arani, H. Khodashenas, and A. R. Ashrafi, A new method for computing Wiener index of dendrimer nanostars, MATCH Commun. Math. Comput. Chem. 69, 2013, 159-164.

Formula

a(n) = -270 + 2^(n-1)*2055+4^(n-1)*(1323*n-3024).

G.f.: -6*x*(-14-234*x-165*x^2+8*x^3) / ( (2*x-1)*(x-1)*(-1+4*x)^2 ). - R. J. Mathar, Apr 11 2013

Maple

a := proc (n) options operator, arrow: -270+2055*2^(n-1)+4^(n-1)*(1323*n-3024) end proc: seq(a(n), n = 1 .. 20);

Crossrefs

Cf. A221011.

Sequence in context: A370572 A297486 A104674 * A219584 A140903 A219470

Adjacent sequences: A221007 A221008 A221009 * A221011 A221012 A221013

Keyword

nonn

Author

Emeric Deutsch, Mar 28 2013

Status

approved