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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. 0

%I #9 Dec 16 2016 03:11:53

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

%N 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.

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

%D 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]

%e 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.

%Y 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).

%K nonn

%O 1,2

%A _Johan de Ruiter_, Feb 04 2010

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