A129130 Number of triples of standard tableaux with the same shape of height less than or equal to three.
1, 1, 2, 10, 63, 531, 6201, 70477, 897149, 12772405, 188334604, 2939523104, 47902337803, 809518276503, 14134544880444, 252955559204532, 4651455689358657, 87356706437180529, 1669767921758484702
Offset: 0
Keywords
Examples
f_111 = f_3 = 1, f_21 = 2 therefore a(3) = f_111^3 + f_21^3 + f_3^3 = 1+8+1 = 10
Links
- F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 463-468.
Formula
sum_lambda f_lambda^3 where the sum is over lambda partitions of length less than or equal to 3 and f_lambda is the number of standard tableaux of shape lambda