cp's OEIS Frontend

A320450 Number of strict antichains of sets whose multiset union is an integer partition of n.

%I A320450 #5 Oct 14 2018 09:16:50
%S A320450 1,1,1,3,3,5,10,13,19,28,47,64,98
%N A320450 Number of strict antichains of sets whose multiset union is an integer partition of n.
%e A320450 The a(1) = 1 through a(8) = 19 antichains:
%e A320450   {{1}}  {{2}}  {{3}}      {{4}}      {{5}}      {{6}}
%e A320450                 {{1,2}}    {{1,3}}    {{1,4}}    {{1,5}}
%e A320450                 {{1},{2}}  {{1},{3}}  {{2,3}}    {{2,4}}
%e A320450                                       {{1},{4}}  {{1,2,3}}
%e A320450                                       {{2},{3}}  {{1},{5}}
%e A320450                                                  {{2},{4}}
%e A320450                                                  {{1},{2,3}}
%e A320450                                                  {{2},{1,3}}
%e A320450                                                  {{3},{1,2}}
%e A320450                                                  {{1},{2},{3}}
%e A320450 .
%e A320450   {{7}}          {{8}}
%e A320450   {{1,6}}        {{1,7}}
%e A320450   {{2,5}}        {{2,6}}
%e A320450   {{3,4}}        {{3,5}}
%e A320450   {{1,2,4}}      {{1,2,5}}
%e A320450   {{1},{6}}      {{1,3,4}}
%e A320450   {{2},{5}}      {{1},{7}}
%e A320450   {{3},{4}}      {{2},{6}}
%e A320450   {{1},{2,4}}    {{3},{5}}
%e A320450   {{2},{1,4}}    {{1},{2,5}}
%e A320450   {{4},{1,2}}    {{1},{3,4}}
%e A320450   {{1,2},{1,3}}  {{2},{1,5}}
%e A320450   {{1},{2},{4}}  {{3},{1,4}}
%e A320450                  {{4},{1,3}}
%e A320450                  {{5},{1,2}}
%e A320450                  {{1,2},{1,4}}
%e A320450                  {{1,2},{2,3}}
%e A320450                  {{1},{2},{5}}
%e A320450                  {{1},{3},{4}}
%t A320450 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A320450 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A320450 submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]];
%t A320450 antiQ[s_]:=Select[Tuples[s,2],And[UnsameQ@@#,submultisetQ@@#]&]=={};
%t A320450 Table[Length[Select[Join@@mps/@IntegerPartitions[n],And[UnsameQ@@#,And@@UnsameQ@@@#,antiQ[#]]&]],{n,10}]
%Y A320450 Cf. A001970, A050342, A089259, A258466, A261049, A319719, A319721, A320328, A320331, A320353.
%K A320450 nonn,more
%O A320450 0,4
%A A320450 _Gus Wiseman_, Oct 12 2018