A309799 Number of distinct nonnegative values that can be assumed by the determinant of an n X n matrix whose entries are a permutation of the multiset {1^n,..,n^n}.

1, 2, 13, 147, 2162, 40498, 948618

Offset: 1

Author

Hugo Pfoertner, Aug 29 2019

Keywords

• nonn
• more
• hard

Comments

a(8) >= 27091220. - Hugo Pfoertner, Sep 23 2019

Examples

			a(2) = 2: 0 = det[1,1; 2,2], 3 = det[2,1; 1,2] are the two possible nonnegative values of the determinant.
a(3) = 13, because
   0 = det[1,2,3; 1,2,3; 1,2,3],  1 = det[2,2,1; 3,2,1; 3,3,1],
   2 = det[3,2,3; 1,2,3; 1,1,2],  3 = det[3,3,3; 1,2,2; 1,1,2],
   4 = det[1,3,3; 2,2,1; 1,3,2],  5 = det[2,2,1; 1,3,3; 1,2,3],
   6 = det[1,3,2; 1,2,3; 2,1,3],  7 = det[1,3,1; 1,2,3; 2,2,3],
   8 = det[1,1,2; 3,3,2; 1,3,2], 12 = det[2,3,1; 2,1,3; 3,1,2],
  13 = det[3,3,1; 1,3,2; 2,1,2], 15 = det[2,1,3; 3,1,1; 2,3,2],
  18 = det[2,3,1; 1,2,3; 3,1,2]
are the 13 possible nonnegative values of the determinant.
		

Crossrefs

Cf. A088216, A088217, A301371, A309258, A322576, A327281.