Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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