A227705 The Wiener index of the nanostar dendrimer defined pictorially as G(n) in the Darafsheh et al. reference.

198, 3834, 34434, 230418, 1327410, 7005042, 34949106, 167809266, 783885042, 3587327730, 16158854898, 71878385394, 316494986994, 1381924896498, 5991517716210, 25821420060402, 110707230375666, 472515428744946, 2008808357363442, 8510221225819890

Offset

0,1

Comments

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

References

M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.

Links

Table of n, a(n) for n=0..19.

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

Formula

a(n) = 4^n*(1728*n - 1872) + 2340*2^n -270.

G.f.: 18*(11+4*x)*(1+8*x)/((1-x)*(1-2*x)*(1-4*x)^2).

Maple

a := proc (n) options operator, arrow: 4^n*(1728*n-1872)+2340*2^n-270 end proc: seq(a(n), n = 0 .. 22);

Crossrefs

Cf. A227706.

Sequence in context: A075457 A364860 A224452 * A331098 A290933 A278017

Adjacent sequences: A227702 A227703 A227704 * A227706 A227707 A227708

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 29 2013

Status

approved