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A374618 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

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%I A374618 #7 Jul 15 2024 10:20:11
%S A374618 1,1,1,2,6,22,111,695,4920,39881,360242
%N A374618 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
%H A374618 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%F A374618 a(n) <= (n-1)! for n > 0.
%t A374618 a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
%Y A374618 Cf. A000142, A369834.
%Y A374618 Cf. A374279, A374280, A374281, A374282.
%Y A374618 Cf. A374617, A374619, A374620, A374621.
%K A374618 nonn,hard,more
%O A374618 0,4
%A A374618 _Stefano Spezia_, Jul 14 2024