The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326349 Number of non-nesting, topologically connected simple graphs covering {1..n}. 2
 1, 0, 1, 0, 1, 11, 95, 797 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Covering means there are no isolated vertices. Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d. A graph with positive integer vertices is topologically connected if the graph whose vertices are the edges and whose edges are crossing pairs of edges is connected. LINKS EXAMPLE The a(5) = 11 edge-sets:   {13,14,25}   {13,24,25}   {13,24,35}   {14,24,35}   {14,25,35}   {13,14,24,25}   {13,14,24,35}   {13,14,25,35}   {13,24,25,35}   {14,24,25,35}   {13,14,24,25,35} MATHEMATICA croXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; x0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&!nesXQ[#]&&Length[csm[Union[Subsets[#, {1}], Select[Subsets[#, {2}], croXQ]]]]<=1&]], {n, 0, 5}] CROSSREFS The binomial transform is the non-covering case A326293. Topologically connected, covering simple graphs are A324327. Non-crossing, covering simple graphs are A324169. Cf. A000108, A000699, A006125, A054726, A099947, A117662. Cf. A324323, A324328, A326329, A326330, A326339, A326341. Sequence in context: A298925 A016203 A241606 * A318599 A051446 A271632 Adjacent sequences:  A326346 A326347 A326348 * A326350 A326351 A326352 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 30 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)