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A374617
a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
4
1, 1, 1, 2, 6, 21, 111, 710, 4968, 39879, 360952
OFFSET
0,4
FORMULA
a(n) <= (n-1)! for n > 0.
MATHEMATICA
a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 14 2024
STATUS
approved