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A327437
Number of unlabeled antichains of nonempty subsets of {1..n} that are either non-connected or non-covering (spanning edge-connectivity 0).
5
1, 1, 3, 6, 15, 52, 410, 32697
OFFSET
0,3
COMMENTS
An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices.
The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.
FORMULA
a(n > 0) = A306505(n) - A261006(n).
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 antichains:
{} {} {} {}
{{1}} {{1}} {{1}}
{{1},{2}} {{1,2}} {{1,2}}
{{1},{2}} {{1},{2}}
{{1},{2,3}} {{1,2,3}}
{{1},{2},{3}} {{1},{2,3}}
{{1,2},{1,3}}
{{1},{2},{3}}
{{1},{2,3,4}}
{{1,2},{3,4}}
{{1},{2},{3,4}}
{{1},{2},{3},{4}}
{{2},{1,3},{1,4}}
{{1,2},{1,3},{2,3}}
{{4},{1,2},{1,3},{2,3}}
CROSSREFS
Column k = 0 of A327438.
The labeled version is A327355.
The covering case is A327426.
Sequence in context: A322851 A230950 A370888 * A267552 A241269 A102356
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 11 2019
STATUS
approved