A364791 a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 0, 1, 2, ..., n-1.

1, 2, 6, 23, 120, 718, 5005, 40274, 362592, 3627920, 39909484, 478991123

Offset: 1

Author

Stefano Spezia, Aug 08 2023

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix

Crossrefs

Right diagonal of A364790.

Cf. A358323 (minimal determinant), A358324 (maximal determinant), A358326 (minimal permanent), A358327 (maximal permanent).

Programs

Mathematica

a[n_]:=Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n!}], n]; Join[{1}, Array[a, 9, 2]] // Flatten

Extensions

a(10)-a(12) from Andrew Howroyd, Jan 07 2024