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%I A326899 #9 Oct 28 2023 14:56:41
%S A326899 1,0,1,4,41,3048,26894637
%N A326899 Number of unlabeled connectedness systems covering n vertices without singletons.
%C A326899 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 A326899 Non-isomorphic representatives of the a(3) = 4 connectedness systems:
%e A326899 {{1,2,3}}
%e A326899 {{2,3},{1,2,3}}
%e A326899 {{1,3},{2,3},{1,2,3}}
%e A326899 {{1,2},{1,3},{2,3},{1,2,3}}
%Y A326899 The case with singletons is A326871.
%Y A326899 First differences of A072444 (the non-covering case).
%Y A326899 Euler transform of A072445 (the connected case).
%Y A326899 The labeled version is A326877.
%Y A326899 Cf. A072446, A072447, A193674, A323818, A326866, A326867, A326868, A326869, A326870.
%K A326899 nonn,more
%O A326899 0,4
%A A326899 _Gus Wiseman_, Aug 02 2019
%E A326899 a(6) corrected by _Andrew Howroyd_, Oct 28 2023