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Number of unlabeled connectedness systems covering n vertices without singletons.
1

%I #9 Oct 28 2023 14:56:41

%S 1,0,1,4,41,3048,26894637

%N Number of unlabeled connectedness systems covering n vertices without singletons.

%C We define a connectedness system (investigated by Vim van Dam in 2002) to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges.

%e Non-isomorphic representatives of the a(3) = 4 connectedness systems:

%e {{1,2,3}}

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

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

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

%Y The case with singletons is A326871.

%Y First differences of A072444 (the non-covering case).

%Y Euler transform of A072445 (the connected case).

%Y The labeled version is A326877.

%Y Cf. A072446, A072447, A193674, A323818, A326866, A326867, A326868, A326869, A326870.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Aug 02 2019

%E a(6) corrected by _Andrew Howroyd_, Oct 28 2023