The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324328 Number of topologically connected chord graphs on a subset of {1,...,n}. 11
 1, 1, 2, 4, 8, 27, 354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A graph is topologically connected if the graph whose vertices are the edges and whose edges are crossing pairs of edges is connected, where two edges cross each other if they are of the form {{x,y},{z,t}} with x < z < y < t or z < x < t < y. LINKS Table of n, a(n) for n=0..6. FORMULA Binomial transform of A324327. EXAMPLE The a(0) = 1 through a(5) = 27 graphs: {} {} {} {} {} {} {{12}} {{12}} {{12}} {{12}} {{13}} {{13}} {{13}} {{23}} {{14}} {{14}} {{23}} {{15}} {{24}} {{23}} {{34}} {{24}} {{13}{24}} {{25}} {{34}} {{35}} {{45}} {{13}{24}} {{13}{25}} {{14}{25}} {{14}{35}} {{24}{35}} {{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[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; crosscmpts[stn_]:=csm[Union[Subsets[stn, {1}], Select[Subsets[stn, {2}], croXQ]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[crosscmpts[#]]<=1&]], {n, 0, 5}] CROSSREFS Cf. A000108, A000699, A001764, A002061, A007297, A016098, A054726 (non-crossing chord graphs), A099947, A136653, A268814. Cf. A324168, A324169, A324172, A324173, A324323, A324327 (covering case). Sequence in context: A212409 A006399 A326293 * A056800 A302915 A259135 Adjacent sequences: A324325 A324326 A324327 * A324329 A324330 A324331 KEYWORD nonn,more AUTHOR Gus Wiseman, Feb 22 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 July 17 10:03 EDT 2024. Contains 374375 sequences. (Running on oeis4.)