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 A326565 Number of covering antichains of nonempty, non-singleton subsets of {1..n}, all having the same sum. 8
 1, 0, 1, 1, 4, 13, 91, 1318, 73581, 51913025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS An antichain is a finite set of finite sets, none of which is a subset of any other. It is covering if its union is {1..n}. The edge-sums are the sums of vertices in each edge, so for example the edge sums of {{1,3},{2,5},{3,4,5}} are {4,7,12}. LINKS EXAMPLE The a(2) = 1 through a(5) = 13 antichains:   {{1,2}}  {{1,2,3}}  {{1,2,3,4}}      {{1,2,3,4,5}}                       {{1,4},{2,3}}    {{1,2,5},{1,3,4}}                       {{2,4},{1,2,3}}  {{1,3,5},{2,3,4}}                       {{3,4},{1,2,4}}  {{1,4,5},{2,3,5}}                                        {{1,4,5},{1,2,3,4}}                                        {{2,3,5},{1,2,3,4}}                                        {{2,4,5},{1,2,3,5}}                                        {{3,4,5},{1,2,4,5}}                                        {{1,5},{2,4},{1,2,3}}                                        {{2,5},{3,4},{1,2,4}}                                        {{3,5},{1,2,5},{1,3,4}}                                        {{4,5},{1,3,5},{2,3,4}}                                        {{1,4,5},{2,3,5},{1,2,3,4}} 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]]]]; cleq[n_]:=Select[stableSets[Subsets[Range[n], {2, n}], SubsetQ[#1, #2]||Total[#1]!=Total[#2]&], Union@@#==Range[n]&]; Table[Length[cleq[n]], {n, 0, 5}] CROSSREFS Cf. A000372, A006126, A035470, A307249, A321455, A321717, A321718, A326360, A326518, A326534, A326566. Sequence in context: A131590 A281182 A200850 * A041433 A222764 A058014 Adjacent sequences:  A326562 A326563 A326564 * A326566 A326567 A326568 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 13 2019 EXTENSIONS a(9) from Andrew Howroyd, Aug 14 2019 STATUS approved

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Last modified November 27 05:27 EST 2020. Contains 338678 sequences. (Running on oeis4.)