|
|
A224434
|
|
The hyper-Wiener index of the dendrimer D_3[n], defined pictorially in the A. R. Ashrafi et al. reference.
|
|
1
|
|
|
357, 112311, 2540727, 28861191, 239301927, 1663126311, 10343555367, 59654395431, 325892779047, 1709482140711, 8689254356007, 43074112914471, 209214647804967, 999137244521511, 4704103526212647, 21880432615990311, 100713104634651687, 459359353571484711
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|