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

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