A384725 Number of solid standard Young tableaux with n cells, height <= 2, and depth <= 2.

1, 1, 3, 7, 19, 55, 177, 543, 1785, 5893, 20137, 68129, 238041, 829015, 2944829, 10423247, 37540189, 134848851, 490691205, 1781665117, 6540487427, 23967631953, 88616165037, 327138472525, 1216949007955, 4521327136295, 16907134893315, 63150657774413, 237215276913281

Offset

0,3

Comments

a(n) is the number of length n words over the alphabet [4] such that any prefix satisfies c(1) >= c(2), c(1) >= c(3), c(2) >= c(4), and c(3) >= c(4), where c(i) is the number of occurrences of the letter i.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

John Tyler Rascoe, Python code.

Example

a(3) = 7: [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 2, 1], [1, 2, 3], [1, 3, 1], [1, 3, 2].

Prog

(Python) # see links

Crossrefs

Cf. A176129, A207542, A215086, A215087.

Sequence in context: A183120 A100702 A367484 * A224031 A147586 A305197

Adjacent sequences: A384722 A384723 A384724 * A384726 A384727 A384728

Keyword

nonn

Author

John Tyler Rascoe, Jan 01 2026

Extensions

a(16)-a(28) from Alois P. Heinz, Jan 04 2026

Status

approved