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 A326359 Number of maximal antichains of nonempty subsets of {1..n}. 9
 1, 1, 2, 6, 28, 375, 31745 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A set system (set of sets) is an antichain if no element is a subset of any other. LINKS FORMULA For n > 0, a(n) = A326358(n) - 1. EXAMPLE The a(0) = 1 through a(4) = 28 antichains:   {}   {1}    {12}      {123}           {1234}               {1}{2}    {1}{23}         {1}{234}                         {2}{13}         {2}{134}                         {3}{12}         {3}{124}                         {1}{2}{3}       {4}{123}                         {12}{13}{23}    {1}{2}{34}                                         {1}{3}{24}                                         {1}{4}{23}                                         {2}{3}{14}                                         {2}{4}{13}                                         {3}{4}{12}                                         {1}{2}{3}{4}                                         {12}{134}{234}                                         {13}{124}{234}                                         {14}{123}{234}                                         {23}{124}{134}                                         {24}{123}{134}                                         {34}{123}{124}                                         {1}{23}{24}{34}                                         {2}{13}{14}{34}                                         {3}{12}{14}{24}                                         {4}{12}{13}{23}                                         {12}{13}{14}{234}                                         {12}{23}{24}{134}                                         {13}{23}{34}{124}                                         {14}{24}{34}{123}                                         {123}{124}{134}{234}                                         {12}{13}{14}{23}{24}{34} MATHEMATICA stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]]; fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)]; Table[Length[fasmax[stableSets[Subsets[Range[n], {1, n}], SubsetQ]]], {n, 0, 5}] CROSSREFS Antichains of nonempty sets are A014466. Minimal covering antichains are A046165. Maximal intersecting antichains are A007363. Maximal antichains of sets are A326358. Cf. A000372, A003182, A006126, A006602, A014466, A058891, A261005, A305000, A305844, A307249, A326360, A326362, A326363. Sequence in context: A108800 A325507 A306793 * A136639 A284594 A027109 Adjacent sequences:  A326356 A326357 A326358 * A326360 A326361 A326362 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 01 2019 EXTENSIONS a(6) from Andrew Howroyd, Aug 14 2019 STATUS approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)