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

Author

N. J. A. Sloane, Apr 07 2017

Keywords

• nonn
• tabl
• more

Examples

			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,
  ...
		

Links

• 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.

Crossrefs

Cf. A281731.

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