

A326209


Number of nesting labeled digraphs with vertices {1..n}.


17




OFFSET

0,3


COMMENTS

Two edges (a,b), (c,d) are nesting if a < c and b > d or a > c and b < d.
Also unsortable digraphs with vertices {1..n}, where a digraph is sortable if, when the edges are listed in lexicographic order, their targets are weakly increasing.
Also the number of semicrossing digraphs with vertices {1..n}, where two edges (a,b), (c,d) are semicrossing if a < c and b < d or a > c and b > d. For example, the a(2) = 4 semicrossing digraph edgesets are:
{11,22}
{11,12,22}
{11,21,22}
{11,12,21,22}


LINKS

Table of n, a(n) for n=0..4.


FORMULA

A002416(n) = a(n) + A326237(n).


EXAMPLE

The a(2) = 4 nesting digraph edgesets:
{12,21}
{11,12,21}
{12,21,22}
{11,12,21,22}


MATHEMATICA

Table[Length[Select[Subsets[Tuples[Range[n], 2]], !OrderedQ[Last/@#]&]], {n, 4}]


CROSSREFS

Nonnesting digraphs are A326237.
Nesting set partitions are A016098.
MMnumbers of nesting multiset partitions are A326256.
MMnumbers of unsortable multiset partitions are A326258.
Cf. A000108, A001519, A002416, A229865.
Cf. A326210, A326211, A326243, A326246, A326248, A326250.
Sequence in context: A259049 A280791 A198709 * A287965 A215647 A228242
Adjacent sequences: A326206 A326207 A326208 * A326210 A326211 A326212


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 19 2019


STATUS

approved



