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A326209 Number of nesting labeled digraphs with vertices {1..n}. 17
0, 0, 4, 408, 64528 (list; graph; refs; listen; history; text; internal format)
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 edge-sets 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 edge-sets:

  {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

Non-nesting digraphs are A326237.

Nesting set partitions are A016098.

MM-numbers of nesting multiset partitions are A326256.

MM-numbers 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

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)