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a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.
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%I #11 Feb 11 2024 11:21:10

%S 1,1,2,6,24,116,717,5033,40301,362845

%N a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.

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

%F a(n) <= A000142(n).

%t a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]

%o (Python)

%o from itertools import permutations

%o from sympy import primerange, prime, Matrix

%o def A369832(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(primerange(prime(n)+1))}) if n else 1 # _Chai Wah Wu_, Feb 11 2024

%Y Cf. A000142, A348891, A350955, A350956.

%Y Cf. A369830, A369831, A369833, A369834, A369835.

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Feb 03 2024