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A374281 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.

%I A374281 #14 Jul 07 2024 05:46:25
%S A374281 1,0,1,8,44,946,27495,592100,25369920,1246207300,55400732937
%N A374281 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 A374281 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%F A374281 a(n) = max(abs(A374279(n)), A374280(n)).
%e A374281 a(5) = 946:
%e A374281   [0, 1, 4, 2, 3]
%e A374281   [1, 0, 1, 4, 2]
%e A374281   [4, 1, 0, 1, 4]
%e A374281   [2, 4, 1, 0, 1]
%e A374281   [3, 2, 4, 1, 0]
%t A374281 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 A374281 Cf. A085750, A351609.
%Y A374281 Cf. A085807 (minimal permanent), A374279 (minimal), A374280 (maximal), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).
%K A374281 nonn,hard,more
%O A374281 0,4
%A A374281 _Stefano Spezia_, Jul 02 2024