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a(n) is the maximal absolute value 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.
5

%I #14 Jul 07 2024 05:46:25

%S 1,0,1,8,44,946,27495,592100,25369920,1246207300,55400732937

%N a(n) is the maximal absolute value 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.

%F a(n) = max(abs(A374279(n)), A374280(n)).

%e a(5) = 946:

%e [0, 1, 4, 2, 3]

%e [1, 0, 1, 4, 2]

%e [4, 1, 0, 1, 4]

%e [2, 4, 1, 0, 1]

%e [3, 2, 4, 1, 0]

%t a[0]=1; a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]]],{i,(n-1)!}]]; Array[a,11,0]

%Y Cf. A085750, A351609.

%Y Cf. A085807 (minimal permanent), A374279 (minimal), A374280 (maximal), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

%K nonn,hard,more

%O 0,4

%A _Stefano Spezia_, Jul 02 2024