A338403 Regular triangle read by rows: T(n,k) is the number of (n,k)-Duck words, for n>=1 and 0<=k<=n-1.

1, 2, 3, 5, 23, 14, 14, 131, 233, 84, 42, 664, 2339, 2367, 594, 132, 3166, 18520, 36265, 24714, 4719, 429, 14545, 127511, 408311, 527757, 266219, 40898

Offset

1,2

Comments

See link for the definition of Duck word.

Links

Table of n, a(n) for n=1..28.

Ilani Axelrod-Freed, 312-Avoiding Reduced Valid Hook Configurations and Duck Words, arXiv:2010.11834 [math.CO], 2020. See Definition 5.1 p. 11.

Ryota Inagaki and Dimana Pramatarova, On Weighted and Bounded Multidimensional Catalan Numbers, arXiv:2510.14956 [math.CO], 2025. See p. 12.

Dimana Miroslavova Pramatarova, Investigating the Periodicity of Weighted Catalan Numbers and Generalizing Them to Higher Dimensions, MIT Res. Sci. Instit. (2025). See pp. 15, 17.

Example

Triangle begins:
   1;
   2,   3;
   5,  23,   14;
  14, 131,  233,   84;
  42, 664, 2339, 2367, 594;
  ...

Crossrefs

Cf. A000108 (column 0), A005700 (diagonal), A005789 (row sums), A031970 (column 1).

Sequence in context: A047995 A244862 A373794 * A024782 A024775 A024767

Adjacent sequences: A338400 A338401 A338402 * A338404 A338405 A338406

Keyword

nonn,tabl,more

Author

Michel Marcus, Oct 24 2020

Status

approved