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A364231

a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 1, 2, ..., n.

+0
1

1, 2, 6, 24, 120, 718, 5005, 40274, 362604, 3627915, 39909566, 478991256

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..12.

Wikipedia, Toeplitz Matrix

MATHEMATICA

a[n_]:=Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Range[n]], i]]], {i, n!}], n]; Array[a, 8]

CROSSREFS

Right diagonal of A364230.

Cf. A350953 (minimal determinant), A350954 (maximal determinant), A351019 (minimal permanent), A351020 (maximal permanent), A356865 (minimal nonzero absolute value determinant).

KEYWORD

nonn,hard,more

AUTHOR

Stefano Spezia, Jul 14 2023

EXTENSIONS

a(10)-a(12) from Andrew Howroyd, Dec 30 2023

STATUS

approved

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