A374279 - OEIS

A374279

a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

1, 0, -1, 4, -44, -946, -8281, -592100, -25369920, -511563816, -55400732937

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..10.

Wikipedia, Toeplitz Matrix.

EXAMPLE

a(5) = -946:

[0, 1, 4, 2, 3]

[1, 0, 1, 4, 2]

[4, 1, 0, 1, 4]

[2, 4, 1, 0, 1]

[3, 2, 4, 1, 0]

MATHEMATICA

a[0]=1; a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n-1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]

CROSSREFS

Cf. A085750, A358323.

Cf. A085807 (minimal permanent), A374280 (maximal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Sequence in context: A206686 A302909 A053333 * A301942 A348130 A255928

Adjacent sequences: A374276 A374277 A374278 * A374280 A374281 A374282

KEYWORD

sign,hard,more

AUTHOR

Stefano Spezia, Jul 02 2024

STATUS

approved