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 A319255 Number of strict antichains of multisets whose multiset union is an integer partition of n. 0
 1, 1, 2, 4, 7, 13, 23, 41, 70, 123, 208, 355, 597 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..12. Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004). EXAMPLE The a(1) = 1 through a(6) = 23 antichains: {{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},{2}} {{1,1,2}} {{1,1,3}} {{3,3}} {{1},{3}} {{1,2,2}} {{1,1,4}} {{1,1,1,1}} {{1},{4}} {{1,2,3}} {{2},{1,1}} {{2},{3}} {{1},{5}} {{1,1,1,2}} {{2,2,2}} {{1},{2,2}} {{2},{4}} {{3},{1,1}} {{1,1,1,3}} {{1,1,1,1,1}} {{1,1,2,2}} {{1,1},{1,2}} {{1},{2,3}} {{2},{1,1,1}} {{2},{1,3}} {{3},{1,2}} {{4},{1,1}} {{1,1,1,1,2}} {{1,1},{1,3}} {{1,1},{2,2}} {{1},{2},{3}} {{3},{1,1,1}} {{1,1,1,1,1,1}} {{1,2},{1,1,1}} {{2},{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]]]]; 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@@#, antiQ[#]]&]], {n, 10}] CROSSREFS Cf. A001970, A258466, A261049, A319719, A319721, A320353, A320355, A320356. Sequence in context: A168043 A114832 A239553 * A136299 A208354 A003116 Adjacent sequences: A319252 A319253 A319254 * A319256 A319257 A319258 KEYWORD nonn,more AUTHOR Gus Wiseman, Oct 12 2018 STATUS approved

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Last modified October 2 07:23 EDT 2023. Contains 365831 sequences. (Running on oeis4.)