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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 June 13 09:03 EDT 2024. Contains 373383 sequences. (Running on oeis4.)