A326372 Number of intersecting antichains of (possibly empty) subsets of {1..n}.

2, 3, 5, 13, 82, 2647, 1422565, 229809982113, 423295099074735261881

Offset

0,1

Comments

A set system (set of sets) is an antichain if no edge is a subset of any other, and is intersecting if no two edges are disjoint.

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = A001206(n + 1) + 1.

Example

The a(0) = 2 through a(3) = 13 antichains:
  {}    {}     {}       {}
  {{}}  {{}}   {{}}     {{}}
        {{1}}  {{1}}    {{1}}
               {{2}}    {{2}}
               {{1,2}}  {{3}}
                        {{1,2}}
                        {{1,3}}
                        {{2,3}}
                        {{1,2,3}}
                        {{1,2},{1,3}}
                        {{1,2},{2,3}}
                        {{1,3},{2,3}}
                        {{1,2},{1,3},{2,3}}

Crossrefs

The case without empty edges is A001206.

The inverse binomial transform is the spanning case A305844.

The unlabeled case is A306007.

Maximal intersecting antichains are A326363.

Intersecting set systems are A051185.

Cf. A000372, A007363, A014466, A305843, A326361, A326362.

Sequence in context: A074394 A056162 A265785 * A001685 A074691 A139589

Adjacent sequences: A326369 A326370 A326371 * A326373 A326374 A326375

Keyword

nonn,more

Author

Gus Wiseman, Jul 01 2019

Status

approved