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

0,3

Links

Table of n, a(n) for n=0..18.

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

Example

f_111 = f_3 = 1, f_21 = 2 therefore a(3) = f_111^3 + f_21^3 + f_3^3 = 1+8+1 = 10

Crossrefs

Cf. A001006, A005802, A003161.

Sequence in context: A371546 A175962 A183165 * A245519 A303483 A186268

Adjacent sequences: A129127 A129128 A129129 * A129131 A129132 A129133

Keyword

nonn

Author

Mike Zabrocki, Mar 30 2007

Status

approved