cp's OEIS Frontend

A326375 Number of intersecting antichains of subsets of {1..n} with empty intersection (meaning there is no vertex in common to all the edges).

%I A326375 #9 Aug 14 2019 18:26:04
%S A326375 2,2,2,3,29,1961,1379274,229755337550,423295079757497714060
%N A326375 Number of intersecting antichains of subsets of {1..n} with empty intersection (meaning there is no vertex in common to all the edges).
%C A326375 A set system (set of sets) is an antichain if no edge is a subset of any other, and is intersecting if no two edges are disjoint.
%F A326375 a(n) = A326366(n) + 1.
%e A326375 The a(4) = 29 antichains:
%e A326375   {}
%e A326375   {{}}
%e A326375   {{1,2},{1,3},{2,3}}
%e A326375   {{1,2},{1,4},{2,4}}
%e A326375   {{1,3},{1,4},{3,4}}
%e A326375   {{2,3},{2,4},{3,4}}
%e A326375   {{1,2},{1,3},{2,3,4}}
%e A326375   {{1,2},{1,4},{2,3,4}}
%e A326375   {{1,2},{2,3},{1,3,4}}
%e A326375   {{1,2},{2,4},{1,3,4}}
%e A326375   {{1,3},{1,4},{2,3,4}}
%e A326375   {{1,3},{2,3},{1,2,4}}
%e A326375   {{1,3},{3,4},{1,2,4}}
%e A326375   {{1,4},{2,4},{1,2,3}}
%e A326375   {{1,4},{3,4},{1,2,3}}
%e A326375   {{2,3},{2,4},{1,3,4}}
%e A326375   {{2,3},{3,4},{1,2,4}}
%e A326375   {{2,4},{3,4},{1,2,3}}
%e A326375   {{1,2},{1,3,4},{2,3,4}}
%e A326375   {{1,3},{1,2,4},{2,3,4}}
%e A326375   {{1,4},{1,2,3},{2,3,4}}
%e A326375   {{2,3},{1,2,4},{1,3,4}}
%e A326375   {{2,4},{1,2,3},{1,3,4}}
%e A326375   {{3,4},{1,2,3},{1,2,4}}
%e A326375   {{1,2},{1,3},{1,4},{2,3,4}}
%e A326375   {{1,2},{2,3},{2,4},{1,3,4}}
%e A326375   {{1,3},{2,3},{3,4},{1,2,4}}
%e A326375   {{1,4},{2,4},{3,4},{1,2,3}}
%e A326375   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
%t A326375 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]]]];
%t A326375 Table[Length[Select[stableSets[Subsets[Range[n]],Or[Intersection[#1,#2]=={},SubsetQ[#1,#2]]&],#=={}||Intersection@@#=={}&]],{n,0,4}]
%Y A326375 The case without empty edges is A326366.
%Y A326375 Intersecting antichains are A326372.
%Y A326375 Antichains of nonempty sets with empty intersection are A006126 or A307249.
%Y A326375 Cf. A001206, A007363, A014466, A051185, A058891, A305001, A305843, A305844, A318128, A318129, A326363, A326365, A326373.
%K A326375 nonn,more
%O A326375 0,1
%A A326375 _Gus Wiseman_, Jul 03 2019
%E A326375 a(7)-a(8) from _Andrew Howroyd_, Aug 14 2019