A305854 - OEIS

%I #10 Aug 13 2019 22:25:17

%S 1,1,2,10,110,14868

%N Number of unlabeled spanning intersecting set-systems on n vertices.

%C An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.

%F a(n) = A305856(n) - A305856(n-1) for n > 0. - _Andrew Howroyd_, Aug 12 2019

%e Non-isomorphic representatives of the a(3) = 10 spanning intersecting set-systems:

%e   {{1,2,3}}

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

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

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

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

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

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

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

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

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

%Y Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305855-A305857.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jun 11 2018

%E a(5) from _Andrew Howroyd_, Aug 12 2019