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A238093
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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).
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0
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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
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OFFSET
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1,13
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LINKS
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Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, Julian West, The Dyck pattern poset, Discrete Math. 321 (2014), 12--23. MR3154009.
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EXAMPLE
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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, ...
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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