login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Andrew Howroyd, Table of n, a(n) for n = 4..50

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

Cf. A006125, A038094, A038095, A038097.

Sequence in context: A248072 A247998 A208707 * A278704 A275141 A275036

Adjacent sequences:  A038093 A038094 A038095 * A038097 A038098 A038099

KEYWORD

nonn,easy,changed

AUTHOR

Christian G. Bower, Jan 04 1999

EXTENSIONS

Edited by N. J. A. Sloane, Sep 14 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)