The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326338 Number of simple graphs with vertices {1..n} whose weakly nesting edges are connected. 5
 1, 1, 2, 7, 48, 781, 27518 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Two edges {a,b}, {c,d} are weakly nesting if a <= c < d <= b or c <= a < b <= d. A graph has its weakly nesting edges connected if the graph whose vertices are the edges and whose edges are weakly nesting pairs of edges is connected. LINKS Table of n, a(n) for n=0..6. Gus Wiseman, The a(4) = 48 weakly nesting-connected graphs. MATHEMATICA wknXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; (x<=z&&y>=t)||(x>=z&&y<=t)]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[csm[Union[List/@#, Select[Subsets[#, {2}], wknXQ]]]]<=1&]], {n, 0, 5}] CROSSREFS The inverse binomial transform is the covering case A326337. The non-weak case is A326330. Cf. A006125, A099947, A136653, A324328, A326289, A326293, A326331, A326335, A326336, A326341. Sequence in context: A304968 A281263 A206153 * A119668 A101538 A045598 Adjacent sequences: A326335 A326336 A326337 * A326339 A326340 A326341 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 29 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 13 10:09 EDT 2024. Contains 373383 sequences. (Running on oeis4.)