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a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
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%I #7 Jul 15 2024 10:20:27

%S 1,1,1,2,6,21,111,710,4968,39879,360952

%N a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

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

%F a(n) <= (n-1)! for n > 0.

%t a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]

%Y Cf. A000142, A369830.

%Y Cf. A374239, A374240, A374241, A374242.

%Y Cf. A374618, A374619, A374620, A374621.

%K nonn,hard,more

%O 0,4

%A _Stefano Spezia_, Jul 14 2024