A109741 Number of inequivalent (completed) n^2 X n^2 sudokus (or Sudokus).

1, 1, 2, 5472730538

Offset

0,3

Comments

See A107739 for definition of an n^2 X n^2 sudoku.

a(2) = 2 independently computed by Gary McGuire and Hugo van der Sanden.

For the 9 X 9 case the allowed equivalences are (see link to Jarvis et al.):

- relabeling entries; reflection; rotation;

- permutation of blocks of columns 1-3, 4-6 and 7-9;

- permutation of blocks of rows 1-3, 4-6 and 7-9;

- permutation of columns 1-3; permutation of rows 1-3;

- permutation of columns 4-6; permutation of rows 4-6;

- permutation of columns 7-9; permutation of rows 7-9.

See A107739 for the total number of ("square") sudoku grids, A114288 for the lexicographically earliest 9 X 9 solution. - M. F. Hasler, Mar 29 2013

References

J.-P. Delahaye, "Le tsunami du Sudoku" in 'Pour La Science' (French Edition of "Scientific American"), December 2005 pp. 144-9, Paris.

Links

Table of n, a(n) for n=0..3.

J. P. Grossman, Javascript Sudoku solver

S. Gupta, Exploring the Mathematics of Su Doku

Frazer Jarvis et al., Sudoku enumeration problems

Eric Weisstein's World of Mathematics, Sudoku

Wikipedia, Sudoku

Example

a(2) = 2:
12|34 12|34
34|12 34|12
--+-- --+--
21|43 23|41
43|21 41|23

Crossrefs

Sequence in context: A306499 A051241 A094486 * A105759 A154422 A154423

Adjacent sequences: A109738 A109739 A109740 * A109742 A109743 A109744

Keyword

nonn,bref,hard,changed

Author

N. J. A. Sloane, Aug 13 2005

Extensions

Links to Jarvis et al. fixed by M. F. Hasler, Mar 29 2013

Status

approved