A301922 -id:A301922 - cp's OEIS frontend

A320606 Regular triangle read by rows where T(n,k) is the number of k-uniform hypergraphs spanning n labeled vertices where every two vertices appear together in some edge, n >= 0, 0 <= k <= n.

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 5, 1, 0, 0, 1, 388, 16, 1, 0, 0, 1, 477965, 27626, 42, 1

Offset: 1

Gus Wiseman, Jan 10 2019

			Triangle begins:
      1
      0      1
      0      0      1
      0      0      1      1
      0      0      1      5      1
      0      0      1    388     16      1
      0      0      1 477965  27626     42      1

Row sums are A321134. Column k = 3 is A302394 without the initial terms.

Cf. A058891, A116539, A301922, A306021, A319189, A320444.

Table[Length[Select[Subsets[If[k==0,{},Subsets[Range[n],{k}]]],And[Union@@#==Range[n],Length[Union@@(Subsets[#,{2}]&/@#)]==Binomial[n,2]]&]],{n,0,6},{k,0,n}]

A320446 Covers of triangles by tetrahedra: number of labeled 4-uniform hypergraphs spanning n vertices such that every three vertices appear together in some edge.

Original entry on oeis.org

1, 1, 1, 0, 1, 6, 5789

Offset: 0

Gus Wiseman, Jan 10 2019

			The a(5) = 6 hypergraphs:
  {{1234},{1235},{1245},{1345}}
  {{1234},{1235},{1245},{2345}}
  {{1234},{1235},{1345},{2345}}
  {{1234},{1245},{1345},{2345}}
  {{1235},{1245},{1345},{2345}}
  {{1234},{1235},{1245},{1345},{2345}}

Cf. A006126, A038041, A299471, A301922, A302374, A302394, A306021, A319540, A320395, A322451.

Table[Length[Select[Subsets[Subsets[Range[n],{4}]],Length[Union@@(Subsets[#,{3}]&/@#)]==Binomial[n,3]&]],{n,6}]

cp's OEIS Frontend

A320606 Regular triangle read by rows where T(n,k) is the number of k-uniform hypergraphs spanning n labeled vertices where every two vertices appear together in some edge, n >= 0, 0 <= k <= n.

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