

A326250


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


11




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<=yz<=x<y<=t];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], wnsXQ]], {n, 0, 5}]


CROSSREFS

Nonnesting set partitions are A000108.
Noncrossing graphs are A054726.
Nesting digraphs are A326209.
Crossing graphs are A326210.
MMnumbers of nesting multiset partitions are A326256.
Cf. A000088, A000332, A006125, A117662.
Cf. A326211, A326243, A326244, A326248, A326257, A326279.
Sequence in context: A099346 A075184 A246283 * A308331 A245141 A203239
Adjacent sequences: A326247 A326248 A326249 * A326251 A326252 A326253


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 21 2019


STATUS

approved



