login
A300056
Number of normal standard domino tableaux whose shape is the integer partition with Heinz number n.
8
1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 3, 1, 0, 0, 3, 0, 3, 2, 1, 0, 0, 0, 0, 1, 0, 3, 1, 0, 4, 2, 0, 0, 1, 0, 0, 1, 0, 1, 6, 0, 0, 3, 1, 0, 4, 0, 5, 0, 0, 0, 1, 1, 8, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 6, 4, 0, 0, 1, 0, 6, 1, 0, 6, 5, 0, 6, 3, 1, 2, 10, 0, 0, 1, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0
OFFSET
1,9
COMMENTS
A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. A tableau is normal if its entries span an initial interval of positive integers. A standard domino tableau is a generalized Young tableau in which all rows and columns are weakly increasing and all regions are dominos. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The a(75) = 6 tableaux:
1 2 4 1 2 3 1 2 2 1 1 4 1 1 4 1 1 3
1 2 4 1 2 3 1 3 3 2 3 4 2 2 4 2 2 3
3 3 4 4 4 4 2 3 3 3 4 4
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 23 2018
STATUS
approved