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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330054 Number of non-isomorphic set-systems of weight n with no endpoints. 9
1, 0, 0, 0, 1, 0, 4, 4, 16, 26, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

A set-system is a finite set of finite nonempty set of positive integers. An endpoint is a vertex appearing only once (degree 1). The weight of a set-system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

LINKS

Table of n, a(n) for n=0..10.

Wikipedia, Degree (graph theory)

EXAMPLE

Non-isomorphic representatives of the a(0) = 1 through a(8) = 16 multiset partitions (empty columns not shown):

  0  {1}{2}{12}  {12}{13}{23}    {13}{23}{123}      {12}{134}{234}

                 {1}{23}{123}    {1}{3}{23}{123}    {1}{234}{1234}

                 {1}{2}{13}{23}  {3}{12}{13}{23}    {12}{34}{1234}

                 {1}{2}{3}{123}  {1}{2}{3}{13}{23}  {1}{12}{34}{234}

                                                    {12}{13}{24}{34}

                                                    {1}{2}{134}{234}

                                                    {1}{2}{34}{1234}

                                                    {2}{13}{14}{234}

                                                    {2}{13}{23}{123}

                                                    {3}{13}{23}{123}

                                                    {1}{2}{13}{24}{34}

                                                    {1}{2}{3}{14}{234}

                                                    {1}{2}{3}{23}{123}

                                                    {1}{2}{3}{4}{1234}

                                                    {2}{3}{12}{13}{23}

                                                    {1}{2}{3}{4}{12}{34}

CROSSREFS

The complement is counted by A330052.

The multiset partition version is A302545.

Non-isomorphic set-systems with no singletons are A306005.

Non-isomorphic set-systems counted by vertices are A000612.

Non-isomorphic set-systems counted by weight are A283877.

Cf. A007716, A055621, A317533, A317794, A319559, A320665, A330055, A330056, A330058.

Sequence in context: A053441 A065732 A092959 * A183433 A322039 A158101

Adjacent sequences:  A330051 A330052 A330053 * A330055 A330056 A330057

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 30 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 October 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)