A319079 Number of connected antichains of sets whose multiset union is an integer partition of n.

1, 1, 2, 3, 4, 4, 8, 7, 12, 15, 19, 26, 43

Offset: 0

Author

Gus Wiseman, Oct 12 2018

Keywords

• nonn
• more

Examples

			The a(10) = 19 clutters:
  {{10}}
  {{1,9}}
  {{2,8}}
  {{3,7}}
  {{4,6}}
  {{1,2,7}}
  {{1,3,6}}
  {{1,4,5}}
  {{2,3,5}}
  {{1,2,3,4}}
  {{5},{5}}
  {{1,2},{1,6}}
  {{1,2},{2,5}}
  {{1,3},{1,5}}
  {{1,4},{1,4}}
  {{2,3},{2,3}}
  {{1,2},{1,2},{1,3}}
  {{2},{2},{2},{2},{2}}
  {{1},{1},{1},{1},{1},{1},{1},{1},{1},{1}}
		

Crossrefs

Cf. A001970, A007718, A048143, A056156, A089259, A319719, A320351, A320353, A320355, A320356.

Programs

Mathematica

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Union[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{_,x_,W___}}/;submultisetQ[{Z},{W}]]];
antiQ[s_]:=Select[Tuples[s,2],And[UnsameQ@@#,submultisetQ@@#]&]=={};
Table[Length[Select[Join@@mps/@IntegerPartitions[n],And[And@@UnsameQ@@@#,Length[csm[#]]==1,antiQ[#]]&]],{n,10}]