A322064 Number of ways to choose a stable partition of a simple connected graph with n vertices.
1, 1, 1, 7, 141, 6533, 631875, 123430027, 48659732725, 39107797223409, 64702785181953175, 221636039917857648631, 1575528053913118966200441, 23249384407499950496231003021, 711653666389829384034090082068939, 45128328085994437067694854477617868995
Offset: 0
Keywords
Examples
The a(3) = 7 stable partitions. The simple connected graph is on top, and below is a list of all its stable partitions. {1,3}{2,3} {1,2}{2,3} {1,2}{1,3} {1,2}{1,3}{2,3} -------- -------- -------- -------- {{1,2},{3}} {{1,3},{2}} {{1},{2,3}} {{1},{2},{3}} {{1},{2},{3}} {{1},{2},{3}} {{1},{2},{3}}
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..75
Crossrefs
Programs
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Mathematica
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Union[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]]; Table[Sum[Length[Select[Subsets[Complement[Subsets[Range[n],{2}],Union@@Subsets/@stn]],And[Union@@#==Range[n],Length[csm[#]]==1]&]],{stn,sps[Range[n]]}],{n,5}]
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PARI
\\ See A322278 for M. seq(n)={concat([1], (M(n)*vectorv(n,i,1))~)} \\ Andrew Howroyd, Dec 01 2018
Extensions
Terms a(7) and beyond from Andrew Howroyd, Dec 01 2018
Comments