A305855 - OEIS

%I #14 May 11 2020 09:43:21

%S 1,1,1,3,9,72,3441,47170585

%N Number of unlabeled spanning intersecting antichains on n vertices.

%C 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.

%F a(n) = A305857(n) - A305857(n-1) for n > 0. - _Andrew Howroyd_, Aug 13 2019

%e Non-isomorphic representatives of the a(4) = 9 spanning intersecting antichains:

%e   {{1,2,3,4}}

%e   {{1,4},{2,3,4}}

%e   {{1,3,4},{2,3,4}}

%e   {{1,2},{1,3,4},{2,3,4}}

%e   {{1,3},{1,4},{2,3,4}}

%e   {{1,4},{2,4},{3,4}}

%e   {{1,2,4},{1,3,4},{2,3,4}}

%e   {{1,2},{1,3},{1,4},{2,3,4}}

%e   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

%Y Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305854-A305857.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Jun 11 2018

%E a(6) from _Andrew Howroyd_, Aug 13 2019

%E a(7) from _Brendan McKay_, May 11 2020