A374281 - OEIS

A374281

a(n) is the maximal absolute value of the 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, 8, 44, 946, 27495, 592100, 25369920, 1246207300, 55400732937

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OFFSET

0,4

LINKS

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

Wikipedia, Toeplitz Matrix.

FORMULA

a(n) = max(abs(A374279(n)), A374280(n)).

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

CROSSREFS

Cf. A085750, A351609.

Cf. A085807 (minimal permanent), A374279 (minimal), A374280 (maximal), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Sequence in context: A129553 A174643 A181268 * A361490 A075863 A118838

Adjacent sequences: A374278 A374279 A374280 * A374282 A374283 A374284

KEYWORD

nonn,hard,more

AUTHOR

Stefano Spezia, Jul 02 2024

STATUS

approved