A364791 - OEIS

A364791

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

%I #10 Jan 08 2024 01:09:35

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

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>

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

%Y Right diagonal of A364790.

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

%K nonn,hard,more

%O 1,2

%A _Stefano Spezia_, Aug 08 2023

%E a(10)-a(12) from _Andrew Howroyd_, Jan 07 2024