A318394 Number of finite sets of set partitions of {1,...,n} such that any two have meet {{1},...,{n}}.

2, 4, 18, 316, 37492

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Example

The a(3) = 18 sets of set partitions:
        0
    {{1,2,3}}
   {{1,3},{2}}
   {{1,2},{3}}
   {{1},{2,3}}
  {{1},{2},{3}}
   {{1,2},{3}}   {{1,3},{2}}
   {{1},{2,3}}   {{1,3},{2}}
   {{1},{2,3}}   {{1,2},{3}}
  {{1},{2},{3}}   {{1,2,3}}
  {{1},{2},{3}}  {{1,3},{2}}
  {{1},{2},{3}}  {{1,2},{3}}
  {{1},{2},{3}}  {{1},{2,3}}
   {{1},{2,3}}   {{1,2},{3}}  {{1,3},{2}}
  {{1},{2},{3}}  {{1,2},{3}}  {{1,3},{2}}
  {{1},{2},{3}}  {{1},{2,3}}  {{1,3},{2}}
  {{1},{2},{3}}  {{1},{2,3}}  {{1,2},{3}}
  {{1},{2},{3}}  {{1},{2,3}}  {{1,2},{3}}  {{1,3},{2}}

Mathematica

stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
spmeet[a_, b_]:=DeleteCases[Union@@Outer[Intersection, a, b, 1], {}]; spmeet[a_, b_, c__]:=spmeet[spmeet[a, b], c];
Table[Length[stableSets[sps[Range[n]], Max@@Length/@spmeet[#1, #2]>1&]], {n, 5}]

Crossrefs

Cf. A000110, A000258, A008277, A059849, A060639, A096827, A181939.

Cf. A318389, A318390, A318391, A318392, A318531, A318532, A318531, A318532.

Sequence in context: A213793 A287612 A308755 * A228933 A347514 A306193

Adjacent sequences: A318391 A318392 A318393 * A318395 A318396 A318397

Keyword

nonn,more

Author

Gus Wiseman, Aug 25 2018

Status

approved