

A305844


Number of labeled spanning intersecting antichains on n vertices.


37




OFFSET

0,4


COMMENTS

An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. S is spanning if every vertex is contained in some edge.


LINKS

Table of n, a(n) for n=0..8.
Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.


FORMULA

Inverse binomial transform of A001206(n + 1).


EXAMPLE

The a(3) = 5 spanning intersecting antichains:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}


MATHEMATICA

Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]], And[Union@@#==Range[n], FreeQ[Intersection@@@Tuples[#, 2], {}, {1}], Select[Tuples[#, 2], UnsameQ@@#&&Complement@@#=={}&]=={}]&], {n, 1, 4}]


CROSSREFS

Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305843.
Sequence in context: A082100 A299353 A180976 * A303132 A070995 A063803
Adjacent sequences: A305841 A305842 A305843 * A305845 A305846 A305847


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jun 11 2018


STATUS

approved



