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

1,2

Comments

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

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]

Links

Table of n, a(n) for n=1..7.

Example

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.

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).

Sequence in context: A024257 A152653 A344693 * A087315 A081460 A327040

Adjacent sequences: A172475 A172476 A172477 * A172479 A172480 A172481

Keyword

nonn

Author

Johan de Ruiter, Feb 04 2010

Status

approved