A224434 The hyper-Wiener index of the dendrimer D_3[n], defined pictorially in the A. R. Ashrafi et al. reference.

357, 112311, 2540727, 28861191, 239301927, 1663126311, 10343555367, 59654395431, 325892779047, 1709482140711, 8689254356007, 43074112914471, 209214647804967, 999137244521511, 4704103526212647, 21880432615990311, 100713104634651687, 459359353571484711

Offset

0,1

Comments

a(0) and a(1) have been checked by the direct computation of the hyper-Wiener index (using Maple).

References

A. R. Ashrafi and H. Shabani, Computing Padmakar-Ivan index of four classes of dendrimers, Bulgarian Chem. Comm., 44, N0. 2, 2012, 127-130.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = 107559 - 551400*2^n + 108900*4^n*n^2 + 444198*4^n -304590*4^n*n + 74910*2^n*n - 18150*2^n*n^2.

G.f. = 3(119+35176z+153456z^2-931008z^3+391824z^4+1360960z^5-42496z^6)/[(1-z)(1-2z)^3(1-4z)^3].

Maple

a := proc (n) options operator, arrow: 107559-551400*2^n + 108900*4^n*n^2 + 444198*4^n - 304590*4^n*n + 74910*2^n*n - 18150*2^n*n^2 end proc: seq(a(n), n = 0 .. 17);

Mathematica

Table[107559-551400*2^n+108900*4^n*n^2+444198*4^n-304590*4^n*n+74910*2^n*n-18150*2^n*n^2, {n, 0, 20}] (* Harvey P. Dale, May 12 2024 *)

Crossrefs

Cf. A224433

Sequence in context: A241931 A166916 A166913 * A278412 A278632 A108875

Adjacent sequences: A224431 A224432 A224433 * A224435 A224436 A224437

Keyword

nonn

Author

Emeric Deutsch, Apr 06 2013

Status

approved