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A374242
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a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 1 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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3,3
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COMMENTS
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The offset is 3 because for n = 2 the unique symmetric Toeplitz matrix having 1 on the main diagonal and 1 off-diagonal is singular.
Conjecture: all the terms are odd.
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LINKS
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EXAMPLE
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a(5) = 3:
[1, 1, 2, 3, 4]
[1, 1, 1, 2, 3]
[2, 1, 1, 1, 2]
[3, 2, 1, 1, 1]
[4, 3, 2, 1, 1]
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MATHEMATICA
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a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]]], {i, (n-1)!}], Positive]]; Array[a, 8, 3]
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CROSSREFS
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KEYWORD
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nonn,hard,more,new
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AUTHOR
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STATUS
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approved
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