A309984 Number of n X n Latin squares with determinant 0, divided by 2.

0, 0, 0, 16, 0, 2088, 5752, 199600889

Offset: 1

Author

Hugo Pfoertner, Aug 26 2019

Keywords

• nonn
• more
• hard

Examples

			a(4)=16: There are 2*a(4) = 32 4 X 4 Latin squares with determinant = 0, one of which is
  [1  4  3  2]
  [4  1  2  3]
  [3  2  1  4]
  [2  3  4  1].
An example of a 6 X 6 Latin square with determinant = 0 is
  [1  3  4  6  5  2]
  [3  2  6  5  4  1]
  [4  6  3  2  1  5]
  [6  5  1  3  2  4]
  [5  4  2  1  3  6]
  [2  1  5  4  6  3].
		

Links

• Brendan McKay, Latin squares.
• Hugo Pfoertner, Occurrence counts of determinant values of Latin squares for n=1..8, zipped (2019).

Crossrefs

Cf. A040082, A136609, A221976, A301371, A308853, A309258, A309985.