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A238093 Array read by antidiagonals upwards: T(n,k) (n>=1, k>=0) = number of Dyck paths of semilength k avoiding the pattern U^(n-1) D U D^(n-1). 0

%I

%S 1,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,2,4,1,0,1,1,2,5,4,1,0,1,1,2,5,13,4,

%T 1,0,1,1,2,5,14,25,4,1,0,1,1,2,5,14,41,25,4,1,0,1,1,2,5,14,42,106,25,

%U 4,1,0,1,1,2,5,14,42,131,196,25,4,1,0,1,1,2,5,14,42,132,392,196,25,4,1,0

%N Array read by antidiagonals upwards: T(n,k) (n>=1, k>=0) = number of Dyck paths of semilength k avoiding the pattern U^(n-1) D U D^(n-1).

%H Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, Julian West, <a href="http://dx.doi.org/10.1016/j.disc.2013.12.011">The Dyck pattern poset</a>, Discrete Math. 321 (2014), 12--23. MR3154009.

%e Array begins (the columns correspond to k = 0, 1, 2, ..., the rows to n = 1, 2, 3, ...):

%e 0, 0, 0, 0, 0, 0, 0, 0, 0 ...

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

%e 1, 1, 2, 4, 4, 4, 4, 4, 4 ...

%e 1, 1, 2, 5, 13, 25, 25, 25, 25, ...

%e 1, 1, 2, 5, 14, 41, 106, 196, ...

%e 1, 1, 2, 5, 14, 42, 131, 392, 980, ...

%e 1, 1, 2, 5, 14, 42, 132, 428, 1380, ...

%e 1, 1, 2, 5, 14, 42, 132, 429, 1429, ...

%e 1, 1, 2, 5, 14, 42, 132, 429, 1430, ...

%e ...

%Y Cf. A000108 (limit of rows).

%K tabl,nonn

%O 1,13

%A _N. J. A. Sloane_, Feb 21 2014

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Last modified October 27 13:13 EDT 2021. Contains 348276 sequences. (Running on oeis4.)