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A374282
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.
5
1, 4, 12, 2, 13, 16, 21, 4, 1
OFFSET
2,2
COMMENTS
The offset is 2 because for n = 1 the matrix is null, and hence, singular.
EXAMPLE
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]
MATHEMATICA
a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n-1]], i]]]]], {i, (n-1)!}], Positive]]; Array[a, 9, 2]
CROSSREFS
Cf. A085807 (minimal permanent), A374279 (minimal signed), A374280 (maximal signed), A374281 (maximal absolute value), A374283 (maximal permanent).
Sequence in context: A016487 A370707 A104063 * A260430 A243347 A317555
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 02 2024
STATUS
approved