A238093 - OEIS

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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).

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

Table of n, a(n) for n=1..91.

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