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%I #7 Jan 10 2019 04:47:02
%S 1,1,1,0,1,6,5789
%N Covers of triangles by tetrahedra: number of labeled 4-uniform hypergraphs spanning n vertices such that every three vertices appear together in some edge.
%e The a(5) = 6 hypergraphs:
%e {{1234},{1235},{1245},{1345}}
%e {{1234},{1235},{1245},{2345}}
%e {{1234},{1235},{1345},{2345}}
%e {{1234},{1245},{1345},{2345}}
%e {{1235},{1245},{1345},{2345}}
%e {{1234},{1235},{1245},{1345},{2345}}
%t Table[Length[Select[Subsets[Subsets[Range[n],{4}]],Length[Union@@(Subsets[#,{3}]&/@#)]==Binomial[n,3]&]],{n,6}]
%Y Cf. A006126, A038041, A299471, A301922, A302374, A302394, A306021, A319540, A320395, A322451.
%K nonn,more
%O 0,6
%A _Gus Wiseman_, Jan 10 2019
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