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A326210 Number of labeled simple graphs with vertices {1..n} containing a nesting pair of edges, where two edges {a,b}, {c,d} are nesting if a < c and b > d or a > c and b < d. 20
0, 0, 0, 0, 16, 672, 29888, 2071936, 268204288, 68717285888, 35184350796800, 36028796807919616, 73786976292712960000, 302231454903635611721728, 2475880078570760326175178752, 40564819207303340845566684397568, 1329227995784915872903782635437883392 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Also simple graphs containing a crossing pair of edges, where two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b.
Also simple graphs such that, if the edges are listed in lexicographic order, their maxima (seconds) are not weakly increasing.
LINKS
FORMULA
A006125(n) = a(n) + A054726(n).
EXAMPLE
The a(4) = 16 nesting edge-sets:
{14,23}
{12,14,23}
{13,14,23}
{14,23,24}
{14,23,34}
{12,13,14,23}
{12,14,23,24}
{12,14,23,34}
{13,14,23,24}
{13,14,23,34}
{14,23,24,34}
{12,13,14,23,24}
{12,13,14,23,34}
{12,14,23,24,34}
{13,14,23,24,34}
{12,13,14,23,24,34}
The a(4) = 16 crossing edge-sets:
{13,24}
{12,13,24}
{13,14,24}
{13,23,24}
{13,24,34}
{12,13,14,24}
{12,13,23,24}
{12,13,24,34}
{13,14,23,24}
{13,14,24,34}
{13,23,24,34}
{12,13,14,23,24}
{12,13,14,24,34}
{12,13,23,24,34}
{13,14,23,24,34}
{12,13,14,23,24,34}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], !OrderedQ[Last/@#]&]], {n, 0, 5}]
PROG
(PARI) seq(n)={my(p=1 + 3/2*x - x^2 - x/2*sqrt(1 - 12*x + 4*x^2 + O(x^n))); concat([0], vector(n, k, 2^binomial(k, 2)-polcoef(p, k)))} \\ Andrew Howroyd, Aug 26 2019
CROSSREFS
Non-nesting graphs are A054726.
Nesting digraphs are A326209.
Nesting (or crossing) set partitions are A016098.
MM-numbers of nesting multiset partitions are A326256.
Sequence in context: A197407 A197429 A231936 * A204841 A264533 A253126
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 19 2019
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Aug 26 2019
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)