A327335 Number of non-isomorphic set-systems with n vertices and at least one endpoint/leaf.

0, 1, 4, 18, 216

Offset

0,3

Comments

A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. A leaf is an edge containing a vertex that does not belong to any other edge, while an endpoint is a vertex belonging to only one edge.

Also covering set-systems with minimum covered vertex-degree 1.

Links

Table of n, a(n) for n=0..4.

Example

Non-isomorphic representatives of the a(1) = 1 through a(3) = 18 set-systems:
  {{1}}  {{1}}        {{1}}
         {{1,2}}      {{1,2}}
         {{1},{2}}    {{1},{2}}
         {{1},{1,2}}  {{1,2,3}}
                      {{1},{1,2}}
                      {{1},{2,3}}
                      {{1},{1,2,3}}
                      {{1,2},{1,3}}
                      {{1},{2},{3}}
                      {{1,2},{1,2,3}}
                      {{1},{2},{1,3}}
                      {{1},{1,2},{1,3}}
                      {{1},{1,2},{2,3}}
                      {{1},{2},{1,2,3}}
                      {{1},{1,2},{1,2,3}}
                      {{1},{2},{3},{1,2}}
                      {{1},{2},{1,2},{1,3}}
                      {{1},{2},{1,2},{1,2,3}}

Crossrefs

Unlabeled set-systems are A000612.

The labeled version is A327228.

The covering version is A327230 (first differences).

Cf. A002494, A245797, A261919, A283877, A327103, A327105, A327197, A327227, A327229, A327336.

Sequence in context: A356561 A197786 A242083 * A275965 A363313 A071173

Adjacent sequences: A327332 A327333 A327334 * A327336 A327337 A327338

Keyword

nonn,more

Author

Gus Wiseman, Sep 02 2019

Status

approved