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A327335
Number of non-isomorphic set-systems with n vertices and at least one endpoint/leaf.
5
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.
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).
Sequence in context: A356561 A197786 A242083 * A275965 A363313 A071173
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 02 2019
STATUS
approved