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 A319079 Number of connected antichains of sets whose multiset union is an integer partition of n. 2
 1, 1, 2, 3, 4, 4, 8, 7, 12, 15, 19, 26, 43 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE 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}} 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}] CROSSREFS Cf. A001970, A007718, A048143, A056156, A089259, A319719, A320351, A320353, A320355, A320356. Sequence in context: A047966 A317085 A236543 * A325329 A224038 A241037 Adjacent sequences:  A319076 A319077 A319078 * A319080 A319081 A319082 KEYWORD nonn,more AUTHOR Gus Wiseman, Oct 12 2018 STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)