cp's OEIS Frontend

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

%I A319079 #18 Oct 14 2018 09:16:40
%S A319079 1,1,2,3,4,4,8,7,12,15,19,26,43
%N A319079 Number of connected antichains of sets whose multiset union is an integer partition of n.
%e A319079 The a(10) = 19 clutters:
%e A319079   {{10}}
%e A319079   {{1,9}}
%e A319079   {{2,8}}
%e A319079   {{3,7}}
%e A319079   {{4,6}}
%e A319079   {{1,2,7}}
%e A319079   {{1,3,6}}
%e A319079   {{1,4,5}}
%e A319079   {{2,3,5}}
%e A319079   {{1,2,3,4}}
%e A319079   {{5},{5}}
%e A319079   {{1,2},{1,6}}
%e A319079   {{1,2},{2,5}}
%e A319079   {{1,3},{1,5}}
%e A319079   {{1,4},{1,4}}
%e A319079   {{2,3},{2,3}}
%e A319079   {{1,2},{1,2},{1,3}}
%e A319079   {{2},{2},{2},{2},{2}}
%e A319079   {{1},{1},{1},{1},{1},{1},{1},{1},{1},{1}}
%t A319079 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A319079 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A319079 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]]]]]]]]];
%t A319079 submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]];
%t A319079 antiQ[s_]:=Select[Tuples[s,2],And[UnsameQ@@#,submultisetQ@@#]&]=={};
%t A319079 Table[Length[Select[Join@@mps/@IntegerPartitions[n],And[And@@UnsameQ@@@#,Length[csm[#]]==1,antiQ[#]]&]],{n,10}]
%Y A319079 Cf. A001970, A007718, A048143, A056156, A089259, A319719, A320351, A320353, A320355, A320356.
%K A319079 nonn,more
%O A319079 0,3
%A A319079 _Gus Wiseman_, Oct 12 2018