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

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