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A374279 a(n) is the minimal 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 A374279 #17 Jul 07 2024 05:45:35
%S A374279 1,0,-1,4,-44,-946,-8281,-592100,-25369920,-511563816,-55400732937
%N A374279 a(n) is the minimal 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 A374279 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374279 a(5) = -946:
%e A374279   [0, 1, 4, 2, 3]
%e A374279   [1, 0, 1, 4, 2]
%e A374279   [4, 1, 0, 1, 4]
%e A374279   [2, 4, 1, 0, 1]
%e A374279   [3, 2, 4, 1, 0]
%t A374279 a[0]=1; a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]],{i,(n-1)!}]]; Array[a,11,0]
%Y A374279 Cf. A085750, A358323.
%Y A374279 Cf. A085807 (minimal permanent), A374280 (maximal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).
%K A374279 sign,hard,more
%O A374279 0,4
%A A374279 _Stefano Spezia_, Jul 02 2024