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A374282
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a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
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5
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OFFSET
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2,2
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COMMENTS
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The offset is 2 because for n = 1 the matrix is null, and hence, singular.
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LINKS
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EXAMPLE
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a(5) = 2:
[0, 4, 1, 2, 3]
[4, 0, 4, 1, 2]
[1, 4, 0, 4, 1]
[2, 1, 4, 0, 4]
[3, 2, 1, 4, 0]
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MATHEMATICA
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a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n-1]], i]]]]], {i, (n-1)!}], Positive]]; Array[a, 9, 2]
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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