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

Author

Michel Marcus, Oct 24 2020

Keywords

• nonn
• tabl
• more
• changed

Comments

See link for the definition of Duck word.

Examples

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

Links

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

Crossrefs

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