A269516 Number of T(n) X T(n) matrices containing the multiset {1, 2, 2, 3, 3, 3, ..., n, n, ..., n} in each row and column, where T(n) = A000217(n).
1, 6, 5450400
Offset: 1
Examples
The a(3) = 5450400 (= 6!*7570) 6 X 6 matrices include
1 2 2 3 3 3
2 1 2 3 3 3
2 2 1 3 3 3
3 3 3 1 2 2
3 3 3 2 1 2
3 3 3 2 2 1.
Using terminology such as that suggested by Rebecca J. Stones in a "Chess Set Latin Square" comment, this matrix is a (3, 2, 1)-frequency square corresponding to a decomposition of K_{6,6} into one 3-regular spanning subgraph, one 2-regular spanning subgraph, and one 1-regular spanning subgraph.
Links
- Mathematics Stack Exchange, Chess Set Latin Square
Comments