A327281 -id:A327281 - cp's OEIS frontend

A322576 Least nonnegative integer that cannot be expressed as the determinant of an n X n matrix whose entries are a permutation of the multiset {1^n, ..., n^n}.

0, 1, 9, 139, 2111, 40021, 942937, 27003797

Offset: 1

Hugo Pfoertner, Aug 29 2019

			a(1) = 0 because det[1] = 1.
a(2) = 1 because det[1,1; 2,2] = 0 and det[2,1; 1,2] = 3 are the only determinant values >= 0 that can be made by permuting the matrix entries {1,1, 2,2}.
a(3) = 9, because it is the first missing value in the list of A309799(3) = 13 determinant values corresponding to {1,1,1, 2,2,2, 3,3,3}: 0, 1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 15, 18.

Cf. A088216, A301371, A309258, A309799, A327281.

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}.

Original entry on oeis.org

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

Offset: 1

Hugo Pfoertner, Aug 29 2019

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

			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.

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

cp's OEIS Frontend

A322576 Least nonnegative integer that cannot be expressed as the determinant of an n X n matrix whose entries are a permutation of the multiset {1^n, ..., n^n}.

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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}.

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