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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326871 Number of unlabeled connectedness systems covering n vertices. 7
1, 1, 4, 24, 436, 80460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

We define a connectedness system (investigated by Vim van Dam in 2002) to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges. It is covering if every vertex belongs to some edge.

LINKS

Table of n, a(n) for n=0..5.

EXAMPLE

Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 connectedness systems:

  {}  {{1}}  {{1,2}}          {{1,2,3}}

             {{1},{2}}        {{1},{2,3}}

             {{2},{1,2}}      {{1},{2},{3}}

             {{1},{2},{1,2}}  {{3},{1,2,3}}

                              {{1},{3},{2,3}}

                              {{2,3},{1,2,3}}

                              {{2},{3},{1,2,3}}

                              {{1},{2,3},{1,2,3}}

                              {{1},{2},{3},{2,3}}

                              {{3},{2,3},{1,2,3}}

                              {{1},{2},{3},{1,2,3}}

                              {{1,3},{2,3},{1,2,3}}

                              {{1},{3},{2,3},{1,2,3}}

                              {{2},{3},{2,3},{1,2,3}}

                              {{2},{1,3},{2,3},{1,2,3}}

                              {{3},{1,3},{2,3},{1,2,3}}

                              {{1,2},{1,3},{2,3},{1,2,3}}

                              {{1},{2},{3},{2,3},{1,2,3}}

                              {{1},{2},{1,3},{2,3},{1,2,3}}

                              {{2},{3},{1,3},{2,3},{1,2,3}}

                              {{3},{1,2},{1,3},{2,3},{1,2,3}}

                              {{1},{2},{3},{1,3},{2,3},{1,2,3}}

                              {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

                              {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

CROSSREFS

The non-covering case case without singletons is A072444.

The case without singletons is A326899.

First differences of A326867 (the non-covering case).

Euler transform of A326869 (the connected case).

The labeled case is A326870.

Cf. A072445, A072446, A072447, A193674, A323818, A326866, A326868.

Sequence in context: A167140 A010572 A247737 * A012945 A296398 A166947

Adjacent sequences:  A326868 A326869 A326870 * A326872 A326873 A326874

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 29 2019

EXTENSIONS

a(5) from Andrew Howroyd, Aug 10 2019

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 December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)