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Number of unlabeled intersecting set-systems on up to n vertices.
3

%I #10 Aug 14 2019 01:48:37

%S 1,2,4,14,124,14992

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

%C An intersecting set-system is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection.

%e Non-isomorphic representatives of the a(3) = 14 intersecting set-systems:

%e {}

%e {{1}}

%e {{1,2}}

%e {{1,2,3}}

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

%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, A304982, A304996, A304998, A305843, A305844, A305854-A305857.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, Jun 11 2018

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