A367904 Number of sets of nonempty subsets of {1..n} with only one possible way to choose a sequence of different vertices of each edge.

1, 2, 6, 38, 666

Offset

0,2

Links

Table of n, a(n) for n=0..4.

Example

The set-system Y = {{1},{1,2},{2,3}} has choices (1,1,2), (1,1,3), (1,2,2), (1,2,3), of which only (1,2,3) has all different elements, so Y is counted under a(3).
The a(0) = 1 through a(2) = 6 set-systems:
  {}  {}     {}
      {{1}}  {{1}}
             {{2}}
             {{1},{2}}
             {{1},{1,2}}
             {{2},{1,2}}

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Select[Tuples[#], UnsameQ@@#&]]==1&]], {n, 0, 3}]

Crossrefs

The version for at least one choice is A367902.

The version for no choices is A367903, no singletons A367769, ranks A367907.

These set-systems have ranks A367908, nonzero A367906.

A000372 counts antichains, covering A006126, nonempty A014466.

A003465 counts covering set-systems, unlabeled A055621.

A058891 counts set-systems, unlabeled A000612.

A059201 counts covering T_0 set-systems.

A323818 counts covering connected set-systems, unlabeled A323819.

Cf. A102896, A133686, A283877, A306445, A355741, A367770, A367862, A367869, A367901, A367905.

Sequence in context: A005738 A055704 A005740 * A006536 A057297 A005530

Adjacent sequences: A367901 A367902 A367903 * A367905 A367906 A367907

Keyword

nonn,more

Author

Gus Wiseman, Dec 08 2023

Status

approved