A306021 -id:A306021 - cp's OEIS frontend

A374453 Number of set-systems S composed of nonempty subsets of [n] such that any element k in S appears at most k times.

1, 2, 6, 36, 547, 26672, 5120069, 4581266029, 21912279450653, 627026135401140277, 118043015040470215561725, 158758107128989643461422723149, 1641097327889006717487651007699748392

Offset: 0

John Tyler Rascoe, Jul 08 2024

			In the set-system: {{2, 3, 5},{3, 4, 5},{1, 3},{2}} no element k appears more than k times, so it is counted under a(5) = 26672.
a(n) for n = 0..2 counts the following set-systems:
a(0) = 1: {}.
a(1) = 2: {}, {{1}}.
a(2) = 6: {}, {{1}}, {{2}}, {{1},{2}}, {{1,2}}, {{1,2},{2}}.

John Tyler Rascoe, Python program.

Cf. A036239, A072444, A072445, A306021, A323818.

Python
```
# see linked program
```

a(7)-a(8) from Alois P. Heinz, Jul 09 2024
a(9) from Alois P. Heinz, Jul 15 2024
a(10)-a(12) from Christian Sievers, Jul 17 2024

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

A374453 Number of set-systems S composed of nonempty subsets of [n] such that any element k in S appears at most k times.

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