A374618 - OEIS

A374618

a(n) is the number of distinct values 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, 1, 1, 2, 6, 22, 111, 695, 4920, 39881, 360242

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OFFSET

0,4

LINKS

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

Wikipedia, Toeplitz Matrix.

FORMULA

a(n) <= (n-1)! for n > 0.

MATHEMATICA

a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]

CROSSREFS

Cf. A000142, A369834.

Cf. A374279, A374280, A374281, A374282.

Cf. A374617, A374619, A374620, A374621.

Sequence in context: A174074 A290279 A014371 * A111280 A095817 A370525

Adjacent sequences: A374615 A374616 A374617 * A374619 A374620 A374621

KEYWORD

nonn,hard,more

AUTHOR

Stefano Spezia, Jul 14 2024

STATUS

approved