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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}.
1
1, 2, 13, 147, 2162, 40498, 948618
OFFSET
1,2
COMMENTS
a(8) >= 27091220. - Hugo Pfoertner, Sep 23 2019
EXAMPLE
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
KEYWORD
nonn,more,hard
AUTHOR
Hugo Pfoertner, Aug 29 2019
STATUS
approved