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A238095
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^(n-1) U D.
2
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 4, 1, 0, 1, 1, 2, 5, 6, 1, 0, 1, 1, 2, 5, 13, 8, 1, 0, 1, 1, 2, 5, 14, 28, 10, 1, 0, 1, 1, 2, 5, 14, 41, 48, 12, 1, 0
OFFSET
1,13
LINKS
Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, and 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, ...):
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 2, 4, 6, 8, 10, 12, 14, 16, ...
1, 1, 2, 5, 13, 28, 48, 73, 103, 138, ...
1, 1, 2, 5, 14, 41, 110, 245, 450, 739, ...
1, 1, 2, 5, 14, 42, 131, 397, 1069, 2427, ...
1, 1, 2, 5, 14, 42, ...
...
CROSSREFS
Cf. A000108 (limit of rows). Row k=4 is A225690, k=5 is A225691.
Sequence in context: A029878 A182458 A238093 * A240608 A080934 A320955
KEYWORD
nonn,tabl,more
AUTHOR
N. J. A. Sloane, Feb 21 2014
STATUS
approved