A320356 Number of strict connected antichains of multisets whose multiset union is an integer partition of n.

1, 1, 2, 3, 5, 8, 13, 22, 35, 62, 98, 171, 277

Offset: 0

Author

Gus Wiseman, Oct 11 2018

Keywords

• nonn
• more

Examples

			The a(1) = 1 through a(6) = 13 clutters:
  {{1}}  {{2}}    {{3}}      {{4}}        {{5}}          {{6}}
         {{1,1}}  {{1,2}}    {{1,3}}      {{1,4}}        {{1,5}}
                  {{1,1,1}}  {{2,2}}      {{2,3}}        {{2,4}}
                             {{1,1,2}}    {{1,1,3}}      {{3,3}}
                             {{1,1,1,1}}  {{1,2,2}}      {{1,1,4}}
                                          {{1,1,1,2}}    {{1,2,3}}
                                          {{1,1,1,1,1}}  {{2,2,2}}
                                          {{1,1},{1,2}}  {{1,1,1,3}}
                                                         {{1,1,2,2}}
                                                         {{1,1,1,1,2}}
                                                         {{1,1},{1,3}}
                                                         {{1,1,1,1,1,1}}
                                                         {{1,2},{1,1,1}}
		

Links

• Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).

Crossrefs

Cf. A001970, A007718, A048143, A056156, A258466, A261006, A293994, A318403, A319079, A319719, A319721, A320351, A320353, A320355.

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[UnsameQ@@#,Length[csm[#]]==1,antiQ[#]]&]],{n,8}]