A326951 Number of unlabeled sets of subsets of {1..n} where every covered vertex is the unique common element of some subset of the edges.

2, 4, 8, 40, 2464

Offset

0,1

Comments

Alternatively, these are unlabeled sets of subsets of {1..n} whose dual is a (strict) antichain, also called T_1 sets of subsets. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. An antichain is a set of subsets where no edge is a subset of any other.

Links

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

Formula

a(n) = 2 * A326972(n).

a(n) = Sum_{k = 0..n} A327011(k).

Example

Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:
  {}    {}        {}
  {{}}  {{}}      {{}}
        {{1}}     {{1}}
        {{},{1}}  {{},{1}}
                  {{1},{2}}
                  {{},{1},{2}}
                  {{1},{2},{1,2}}
                  {{},{1},{2},{1,2}}

Crossrefs

Unlabeled sets of subsets are A003180.

Unlabeled T_0 sets of subsets are A326949.

The labeled version is A326967.

The case without empty edges is A326972.

The covering case is A327011 (first differences).

Cf. A003181, A059052, A326960, A326965, A326969, A326974, A326976.

Sequence in context: A319595 A285632 A102918 * A018395 A136538 A018403

Adjacent sequences: A326948 A326949 A326950 * A326952 A326953 A326954

Keyword

nonn,more

Author

Gus Wiseman, Aug 13 2019

Status

approved