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A327355
Number of antichains of nonempty subsets of {1..n} that are either non-connected or non-covering (spanning edge-connectivity 0).
8
1, 1, 4, 14, 83, 1232, 84625, 109147467, 38634257989625
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) = A120338(n) + A014466(n) - A006126(n).
EXAMPLE
The a(1) = 1 through a(3) = 14 antichains:
{} {} {}
{{1}} {{1}}
{{2}} {{2}}
{{1},{2}} {{3}}
{{1,2}}
{{1,3}}
{{2,3}}
{{1},{2}}
{{1},{3}}
{{2},{3}}
{{1},{2,3}}
{{2},{1,3}}
{{3},{1,2}}
{{1},{2},{3}}
CROSSREFS
Column k = 0 of A327352.
The covering case is A120338.
The unlabeled version is A327437.
The non-spanning edge-connectivity version is A327354.
Sequence in context: A355950 A063862 A222497 * A356508 A024421 A259353
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 10 2019
STATUS
approved