A284732 Square array read by antidiagonals downwards: T(n,k) = number of linear extensions of the North-East rectangular partial order NE_{n,k} that avoid the pattern 2143.

1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 14, 21, 8, 1, 1, 42, 121, 89, 16, 1, 1, 132, 728, 1094, 377, 32, 1

Offset

1,5

Links

Table of n, a(n) for n=1..28.

David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, Pattern Avoiding Linear Extensions of Rectangular Posets, arXiv preprint arXiv:1605.06825 [math.CO], 2016.

Example

The square array begins:
  1,  1,   1,    1,      1, ...
  1,  2,   5,   14,     42, ...
  1,  4,  21,  121,    728, ...
  1,  8,  89, 1094,  14041, ...
  1, 16, 377, 9841, 266110, ...
  ...
As a triangular array:
  1,
  1,   1,
  1,   2,   1,
  1,   5,   4,    1,
  1,  14,  21,    8,   1,
  1,  42, 121,   89,  16,  1,
  1, 132, 728, 1094, 377, 32, 1,
  ...

Crossrefs

Cf. A281731.

For early rows and columns see A000108, A000079 and (apparently) A274969, A015448.

Sequence in context: A241500 A152924 A220738 * A371766 A327483 A327884

Adjacent sequences: A284729 A284730 A284731 * A284733 A284734 A284735

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Apr 07 2017

Status

approved