A224453 The hyper-Wiener index of the nanostar dendrimer NS_2[n], defined pictorially in the A. R. Ashrafi et al. reference.

477, 14517, 192133, 1790789, 13716357, 92392837, 568494213, 3272754309, 17914312837, 94292506757, 481127721093, 2394073245829, 11669512054917, 55910670854277, 264011366000773, 1231270134409349, 5680970473662597, 25967383211403397, 117723243179141253

Offset

0,1

Comments

a(2) and a(3) have been checked by the direct computation of the Wiener index (using Maple).

References

A. R. Ashrafi and P. Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = -6011 + (-36208 - 9720n + 2800n^2)*2^n + (42696 -22400n + 6400n^2)*4^n.

G.f.: (477 + 5454z - 12140z^2 + 14440z^3 + 22624z^4 - 202880z^5 + 9728z^6)/((1-z)(1-2z)^3*(1-4z)^3).

Maple

a := proc (n) options operator, arrow: -6011-22400*4^n*n-9720*2^n*n-36208*2^n+42696*4^n+2800*2^n*n^2+6400*4^n*n^2 end proc: seq(a(n), n = 0 .. 18);

Crossrefs

Cf. A224452.

Sequence in context: A278286 A216141 A325822 * A227706 A261816 A352265

Adjacent sequences: A224450 A224451 A224452 * A224454 A224455 A224456

Keyword

nonn

Author

Emeric Deutsch, Apr 06 2013

Status

approved