Voozh

A224423

The Wiener index of the Micelle-like chiral dendrimer G[n] defined pictorially in the Hassan Yousefi-Azari et al. reference.

24485, 120741, 613541, 3078309, 15070373, 71955621, 336069797, 1540900005, 6958417061, 31031755941, 136961328293, 599275078821, 2603021763749, 11236212212901, 48242297406629, 206161018094757, 877415731561637, 3720758807233701, 15727438348682405

(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..18.

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 (13,-64,148,-160,64).

FORMULA

a(n) = 1189 + 15616*2^n + 7680*4^n + 12288*n*4^n + 4224*n*2^n (agrees with Theorem 2 of the Yousefi-Azari et al. reference).

G.f.: (24485-197564*x+610948*x^2-794080*x^3+366912*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2). [Bruno Berselli, Apr 06 2013]

MAPLE

a := proc (n) options operator, arrow: 1189 + 15616*2^n + 4224*2^n*n + 12288*4^n*n + 7680*4^n end proc: seq(a(n), n = 0 .. 18);

MATHEMATICA

CoefficientList[Series[(24485 - 197564 x + 610948 x^2 - 794080 x^3 + 366912 x^4)/((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 20}], x] (* Bruno Berselli, Apr 06 2013 *)

CROSSREFS

Cf. A224424.

Sequence in context: A083621 A083622 A237207 * A356355 A258441 A244150

Adjacent sequences: A224420 A224421 A224422 * A224424 A224425 A224426

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Apr 06 2013

STATUS

approved

URL: https://oeis.org/A224423

⇱ A224423 - OEIS