A284731 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 123.

1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 14, 33, 14, 1, 1, 42, 234, 238, 42, 1, 1, 132, 1706, 4146, 1782, 132, 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, ...
  1,   2,      5,       14,      42,    132, ...
  1,   5,     33,      234,    1706,  12618, ...
  1,  14,    238,     4146,   72152, 126804, ...
  1,  42,   1782,    75187, 3099106, ...
  1, 132,  13593,  1378668, ...
  1, 429, 104756, 25430445, ...
  ...
As a triangular array:
  1,
  1,   1,
  1,   2,    1,
  1,   5,    5,    1,
  1,  14,   33,   14,    1,
  1,  42,  234,  238,   42,   1,
  1, 132, 1706, 4146, 1782, 132, 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. A281732, A281733, A281734.