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| NAME
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allocatedNumber of non-isomorphic set-systems with n vertices and at forleast Gusone Wisemanendpoint/leaf.
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| DATA
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0, 1, 4, 18, 216
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| OFFSET
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0,3
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| COMMENTS
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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.
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| EXAMPLE
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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}}
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| CROSSREFS
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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.
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| KEYWORD
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allocated
nonn,more
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| AUTHOR
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Gus Wiseman, Sep 02 2019
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| STATUS
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approved
editing
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