A369830 - OEIS

%I #12 Feb 12 2024 12:41:51

%S 1,1,2,5,22,97,613,4749,38493,353684

%N a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.

%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[Range[n]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A369830(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(range(1,n+1))}) # _Chai Wah Wu_, Feb 12 2024

%Y Cf. A000142, A350953, A350954, A356865.

%Y Cf. A369831, A369832, A369833, A369834, A369835.

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Feb 03 2024