A326250 Number of weakly nesting simple graphs with vertices {1..n}.

0, 0, 0, 3, 50, 982, 32636, 2096723

Offset

0,4

Comments

Two edges {a,b}, {c,d} are weakly nesting if a <= c < d <= b or c <= a < b <= d.

Links

Table of n, a(n) for n=0..7.

Gus Wiseman, The a(4) = 50 weakly nesting simple graphs.

Formula

Conjecture: A006125(n) = a(n) + A000108(n).

Mathematica

wnsXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<=z<t<=y||z<=x<y<=t];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], wnsXQ]], {n, 0, 5}]

Crossrefs

Non-nesting set partitions are A000108.

Non-crossing graphs are A054726.

Nesting digraphs are A326209.

Crossing graphs are A326210.

MM-numbers of nesting multiset partitions are A326256.

Cf. A000088, A000332, A006125, A117662.

Cf. A326211, A326243, A326244, A326248, A326257, A326279.

Sequence in context: A075184 A337902 A246283 * A308331 A245141 A203239

Adjacent sequences: A326247 A326248 A326249 * A326251 A326252 A326253

Keyword

nonn,more

Author

Gus Wiseman, Jun 21 2019

Status

approved