cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A326329 Number of simple graphs covering {1..n} with no crossing or nesting edges.

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%I A326329 #16 Jul 04 2019 13:57:25
%S A326329 1,0,1,4,13,44,149,504,1705,5768,19513,66012
%N A326329 Number of simple graphs covering {1..n} with no crossing or nesting edges.
%C A326329 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.
%C A326329 Is this (apart from offsets) the same as A073717? - _R. J. Mathar_, Jul 04 2019
%H A326329 Eric Marberg, <a href="http://arxiv.org/abs/1203.5738">Crossings and nestings in colored set partitions</a>, arXiv preprint arXiv:1203.5738 [math.CO], 2012.
%H A326329 Gus Wiseman, <a href="/A326329/a326329.png">The a(5) = 44 covering simple graphs with no crossing or nesting edges</a>.
%t A326329 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Union@@#==Range[n]&&!MatchQ[#,{___,{x_,y_},___,{z_,t_},___}/;x<z<y<t||z<x<t<y||x<z<t<y||z<x<y<t]&]],{n,0,5}]
%Y A326329 The case for set partitions is A001519.
%Y A326329 Covering simple graphs are A006129.
%Y A326329 The case with just nesting or just crossing edges forbidden is A324169.
%Y A326329 The binomial transform is the non-covering case A326244.
%Y A326329 Cf. A000108, A006125, A007297, A054726, A099947, A324327, A326279, A326293.
%K A326329 nonn,more
%O A326329 0,4
%A A326329 _Gus Wiseman_, Jun 27 2019