|
|
A038096
|
|
Number of rooted graphs on n labeled nodes where the root has degree 3.
|
|
5
|
|
|
32, 1280, 61440, 4587520, 587202560, 135291469824, 57724360458240, 46443371157258240, 71337018097548656640, 211030752203237270487040, 1210134745434243803880882176, 13518305228996352601898436526080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
4,1
|
|
COMMENTS
|
The graphs are not necessarily connected. The nodes are labeled.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n*binomial(n-1,3)*2^binomial(n-1,2). (There are n choices for the root, binomial(n-1,3) choices for the nodes it joined to, and 2^binomial(n-1,2) choices for the edges between the non-root nodes.)
|
|
EXAMPLE
|
For n=4, take 4 nodes labeled a,b,c,d. We can choose the root in 4 ways, say a, and it must be joined to b,c,d. Each of the three edges bc, bd, cd may or may not exist, so there are 4*8 = 32 = a(4) possibilities.
|
|
MATHEMATICA
|
Table[n Binomial[n-1, 3] 2^Binomial[n-1, 2], {n, 4, 20}] (* Harvey P. Dale, Sep 14 2011 *)
|
|
PROG
|
(PARI) a(n) = {n*binomial(n-1, 3)*2^binomial(n-1, 2)} \\ Andrew Howroyd, Nov 23 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|