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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.
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%I #17 Jun 17 2017 02:27:09

%S 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,

%T 1782,132,1

%N 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.

%H David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, <a href="http://arxiv.org/abs/1605.06825">Pattern Avoiding Linear Extensions of Rectangular Posets</a>, arXiv preprint arXiv:1605.06825 [math.CO], 2016.

%e The square array begins:

%e 1, 1, 1, 1, 1, 1, ...

%e 1, 2, 5, 14, 42, 132, ...

%e 1, 5, 33, 234, 1706, 12618, ...

%e 1, 14, 238, 4146, 72152, 126804, ...

%e 1, 42, 1782, 75187, 3099106, ...

%e 1, 132, 13593, 1378668, ...

%e 1, 429, 104756, 25430445, ...

%e ...

%e As a triangular array:

%e 1,

%e 1, 1,

%e 1, 2, 1,

%e 1, 5, 5, 1,

%e 1, 14, 33, 14, 1,

%e 1, 42, 234, 238, 42, 1,

%e 1, 132, 1706, 4146, 1782, 132, 1,

%e ...

%Y Cf. A281732, A281733, A281734.

%K nonn,tabl,more

%O 1,5

%A _N. J. A. Sloane_, Apr 07 2017