A238095 - OEIS

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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.

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 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`1,13`
	LINKS	`Table of n, a(n) for n=1..55.` `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` `Adjacent sequences: A238092 A238093 A238094 * A238096 A238097 A238098`
	KEYWORD	`nonn,tabl,more`
	AUTHOR	`N. J. A. Sloane, Feb 21 2014`
	STATUS	`approved`

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Last modified September 17 12:40 EDT 2021. Contains 347477 sequences. (Running on oeis4.)