A221011 The hyper-Wiener index of the nanostar dendrimer G[n], defined pictorially in the Nadjafi-Arani et al. reference.

159, 8934, 138021, 1343571, 10311135, 68588151, 415166631, 2351820039, 12687791559, 65945446215, 332865161799, 1641053851719, 7935696378951, 37761280783431, 177249667277895, 822339653125191, 3776814888617031, 17193456239838279, 77664102465799239, 348399491831563335

Offset

1,1

Comments

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

Links

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

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.

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

Formula

a(n) = 1095-2^(n-2)*33885+4^(n-2)*(15876*n^2-69930*n+118080).

G.f.: -3*x*(160*x^4+1564*x^3+5895*x^2+2183*x+53) / ((x-1)*(2*x-1)*(4*x-1)^3). - Colin Barker, Mar 31 2013

Maple

a := proc (n) options operator, arrow: 1095-33885*2^(n-2)+4^(n-2)*(15876*n^2-69930*n+118080) end proc: seq(a(n), n = 1 .. 20);

Crossrefs

Cf. A221010.

Sequence in context: A293920 A281336 A205164 * A267964 A268029 A263518

Adjacent sequences: A221008 A221009 A221010 * A221012 A221013 A221014

Keyword

nonn,easy

Author

Emeric Deutsch, Mar 28 2013

Status

approved