# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a326574 Showing 1-1 of 1 %I A326574 #6 Aug 13 2019 15:44:57 %S A326574 2,3,5,10,22,61,247,2096,81896,52260575 %N A326574 Number of antichains of subsets of {1..n} with equal edge-sums. %C A326574 An antichain is a finite set of finite sets, none of which is a subset of any other. 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}. %e A326574 The a(0) = 2 through a(4) = 22 antichains: %e A326574 {} {} {} {} {} %e A326574 {{}} {{}} {{}} {{}} {{}} %e A326574 {{1}} {{1}} {{1}} {{1}} %e A326574 {{2}} {{2}} {{2}} %e A326574 {{1,2}} {{3}} {{3}} %e A326574 {{1,2}} {{4}} %e A326574 {{1,3}} {{1,2}} %e A326574 {{2,3}} {{1,3}} %e A326574 {{1,2,3}} {{1,4}} %e A326574 {{3},{1,2}} {{2,3}} %e A326574 {{2,4}} %e A326574 {{3,4}} %e A326574 {{1,2,3}} %e A326574 {{1,2,4}} %e A326574 {{1,3,4}} %e A326574 {{2,3,4}} %e A326574 {{1,2,3,4}} %e A326574 {{3},{1,2}} %e A326574 {{4},{1,3}} %e A326574 {{1,4},{2,3}} %e A326574 {{2,4},{1,2,3}} %e A326574 {{3,4},{1,2,4}} %t A326574 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 A326574 cleqset[set_]:=stableSets[Subsets[set],SubsetQ[#1,#2]||Total[#1]!=Total[#2]&]; %t A326574 Table[Length[cleqset[Range[n]]],{n,0,5}] %Y A326574 Set partitions with equal block-sums are A035470. %Y A326574 Antichains with different edge-sums are A326030. %Y A326574 MM-numbers of multiset partitions with equal part-sums are A326534. %Y A326574 The covering case is A326566. %Y A326574 Cf. A000372, A003182, A006126, A307249, A321455, A321717, A321718, A326518, A326565, A326572. %K A326574 nonn,more %O A326574 0,1 %A A326574 _Gus Wiseman_, Jul 18 2019 %E A326574 a(9) from _Andrew Howroyd_, Aug 13 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE