A364234 a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the first n prime numbers.

1, 2, 6, 24, 120, 718, 5036, 40316, 362862, 3628786, 39916701, 479001517

Offset: 1

Author

Stefano Spezia, Jul 14 2023

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix

Crossrefs

Right diagonal of A364233.

Cf. A348891 (minimal nonzero absolute value determinant), A350955 (minimal determinant), A350956 (maximal determinant), A351021 (minimal permanent), A351022 (maximal permanent).

Programs

Mathematica

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

Extensions

a(10)-a(12) from Andrew Howroyd, Dec 31 2023