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%I #52 Feb 17 2026 09:33:41
%S 1,1,3,7,19,55,177,543,1785,5893,20137,68129,238041,829015,2944829,
%T 10423247,37540189,134848851,490691205,1781665117,6540487427,
%U 23967631953,88616165037,327138472525,1216949007955,4521327136295,16907134893315,63150657774413,237215276913281
%N Number of solid standard Young tableaux with n cells, height <= 2, and depth <= 2.
%C 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.
%H Alois P. Heinz, <a href="/A384725/b384725.txt">Table of n, a(n) for n = 0..300</a>
%H John Tyler Rascoe, <a href="/A384725/a384725_2.py.txt">Python code</a>.
%e a(3) = 7: [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 2, 1], [1, 2, 3], [1, 3, 1], [1, 3, 2].
%o (Python) # see links
%Y Cf. A176129, A207542, A215086, A215087.
%K nonn
%O 0,3
%A _John Tyler Rascoe_, Jan 01 2026
%E a(16)-a(28) from _Alois P. Heinz_, Jan 04 2026