A224428 The hyper-Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference.

1032, 54472, 853256, 8392840, 64852872, 433408392, 2632152456, 14947110280, 80788946312, 420521631112, 2125121035656, 10487138557320, 50753701289352, 241670439050632, 1135046330686856, 5268615489133960, 24208077521689992, 110246366797634952

Offset

0,1

Comments

a(1) has been checked by the direct computation of the Wiener index (using Maple).

References

A. R. Ashrafi and M. Mirzargar, The study of an infinite class of dendrimer nanostars by topological index approaches, J. Appl. Math. Comput, 31, 2009, 289-294.

M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (15,-86,232,-288,128).

Formula

a(n) = 7560 - 64000*4^n*n - 113312*2^n + 106784*4^n + 25600*4^n*n^2.

G.f.: 8*(129+4874*x+15616*x^2+4896*x^3)/((1-x)*(1-2*x)*(1-4*x)^3). [Bruno Berselli, Apr 06 2013]

Maple

a := proc (n) options operator, arrow: 7560-113312*2^n+25600*4^n*n^2-64000*4^n*n+106784*4^n end proc: seq(a(n), n = 0 .. 18);

Mathematica

CoefficientList[Series[8 (129 + 4874 x + 15616 x^2 + 4896 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^3), {x, 0, 20}], x] (* Bruno Berselli, Apr 06 2013 *)

Crossrefs

Cf. A224427.

Sequence in context: A023062 A035046 A282357 * A283724 A168225 A282576

Adjacent sequences: A224425 A224426 A224427 * A224429 A224430 A224431

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 06 2013

Status

approved