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

1,5

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, ...
  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,
  ...

Crossrefs

Cf. A281732, A281733, A281734.

Sequence in context: A187617 A306344 A128612 * A211400 A060854 A091378

Adjacent sequences: A284728 A284729 A284730 * A284732 A284733 A284734

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Apr 07 2017

Status

approved