A172478 The number of ways to dissect an n X n square into polyominoes of size n and then fill it to make it a Latin square, with the extra requirement that each number occurs within each polyomino exactly once.

1, 4, 72, 13872, 11762160, 234312972480, 41182101508222080

Offset: 1

Author

Johan de Ruiter, Feb 04 2010

Keywords

• nonn

Comments

a(n) is the number of completed n X n jigsaw sudoku puzzles.

Examples

			A 2 X 2 square can be covered by two dominoes by either positioning them vertically or horizontally. Both of these coverings allow for two 2 X 2 Latin squares without violating the extra constraint.
		

References

• J. de Ruiter, On Jigsaw Sudoku Puzzles and Related Topics, Bachelor Thesis, Leiden Institute of Advanced Computer Science, 2010. [From Johan de Ruiter, Jun 15 2010]

Crossrefs

Cf. A002860 (Number of Latin squares of order n), A172477 (Number of ways to dissect an n X n square into polyominoes of size n).