A291188 Number of inequivalent 2 X n Sudoku grids ((2*n) X (2*n) grids divided into 2 X n boxes).

2, 49, 1673187, 4743933602050718

Offset: 2

Author

Seiichi Manyama, Aug 19 2017

Keywords

• nonn
• more

Comments

We regard two grids as inequivalent if one cannot be transformed into another by some sequence of symmetries, or by relabeling. For the 2 X 3 Sudoku grids case the allowed equivalences are (see link to Jarvis):

- relabeling entries; reflection; rotation;

- permutation of blocks of columns 1-2, 3-4 and 5-6;

- permutation of blocks of rows 1-3 and 4-6;

- permutation of columns 1-2;

- permutation of columns 3-4;

- permutation of columns 5-6;

- permutation of rows 1-3;

- permutation of rows 4-6.

Examples

			a(2) = 2:
.
  12|34  12|34
  34|12  34|12
  --+--  --+--
  21|43  23|41
  43|21  41|23
.
An example of 2 X 3 Sudoku grids:
.
  14|25|36
  35|16|24
  26|34|15
  --+--+--
  41|52|63
  52|63|41
  63|41|52
		

Links

• Frazer Jarvis, Sudoku enumeration problems
• Jordy Vanpoucke, Mutually orthogonal latin squares and their generalizations

Crossrefs

Cf. A109741, A291187.