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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
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, 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, 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
OFFSET
1,13
LINKS
Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, Julian West, The Dyck pattern poset, Discrete Math. 321 (2014), 12--23. MR3154009.
EXAMPLE
Array begins (the columns correspond to k = 0, 1, 2, ..., the rows to n = 1, 2, 3, ...):
0, 0, 0, 0, 0, 0, 0, 0, 0 ...
1, 1, 1, 1, 1, 1, 1, 1, 1 ...
1, 1, 2, 4, 4, 4, 4, 4, 4 ...
1, 1, 2, 5, 13, 25, 25, 25, 25, ...
1, 1, 2, 5, 14, 41, 106, 196, ...
1, 1, 2, 5, 14, 42, 131, 392, 980, ...
1, 1, 2, 5, 14, 42, 132, 428, 1380, ...
1, 1, 2, 5, 14, 42, 132, 429, 1429, ...
1, 1, 2, 5, 14, 42, 132, 429, 1430, ...
...
CROSSREFS
Cf. A000108 (limit of rows).
Sequence in context: A035440 A029878 A182458 * A238095 A240608 A080934
KEYWORD
tabl,nonn
AUTHOR
N. J. A. Sloane, Feb 21 2014
STATUS
approved