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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 (list; table; graph; refs; listen; history; text; internal format)
 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 Adjacent sequences:  A238090 A238091 A238092 * A238094 A238095 A238096 KEYWORD tabl,nonn AUTHOR N. J. A. Sloane, Feb 21 2014 STATUS approved

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Last modified September 21 10:46 EDT 2021. Contains 347597 sequences. (Running on oeis4.)