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a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the first n prime numbers.
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%I #12 Dec 31 2023 12:43:11

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

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

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

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

%Y Right diagonal of A364233.

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

%K nonn,hard,more

%O 1,2

%A _Stefano Spezia_, Jul 14 2023

%E a(10)-a(12) from _Andrew Howroyd_, Dec 31 2023