A327230 Number of non-isomorphic set-systems covering n vertices with at least one endpoint/leaf.

0, 1, 3, 14, 198

Offset: 0

Author

Gus Wiseman, Sep 01 2019

Keywords

• nonn
• more

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 vertex-degree 1.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(3) = 14 set-systems:
  {{1}}  {{1,2}}      {{1,2,3}}
         {{1},{2}}    {{1},{2,3}}
         {{2},{1,2}}  {{1},{2},{3}}
                      {{1,3},{2,3}}
                      {{3},{1,2,3}}
                      {{1},{3},{2,3}}
                      {{2,3},{1,2,3}}
                      {{2},{1,3},{2,3}}
                      {{2},{3},{1,2,3}}
                      {{3},{1,3},{2,3}}
                      {{1},{2},{3},{2,3}}
                      {{3},{2,3},{1,2,3}}
                      {{2},{3},{1,3},{2,3}}
                      {{2},{3},{2,3},{1,2,3}}
		

Crossrefs

Unlabeled covering set-systems are A055621.

The labeled version is A327229.

The non-covering version is A327335 (partial sums).

Cf. A002494, A245797, A261919, A283877, A327103, A327105, A327197, A327227, A327228.