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A374241 a(n) is the maximal absolute value 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.

%I A374241 #9 Oct 10 2024 07:24:32
%S A374241 1,1,0,1,40,545,13805,526773,18551951,768561384,31451535983,
%T A374241 1273675677456,87868166035113,7601760995500947,664087819207293468
%N A374241 a(n) is the maximal absolute value 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 A374241 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A374239%2B40%2B41%2B42.py">Python program</a>.
%H A374241 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%F A374241 a(n) = max(abs(A374239(n)), A374240(n)).
%e A374241 a(5) = 545:
%e A374241   [1, 1, 4, 2, 3]
%e A374241   [1, 1, 1, 4, 2]
%e A374241   [4, 1, 1, 1, 4]
%e A374241   [2, 4, 1, 1, 1]
%e A374241   [3, 2, 4, 1, 1]
%t A374241 a[0]=1; a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]]], {i, (n-1)!}]]; Array[a, 11, 0]
%Y A374241 Cf. A351609, A374139.
%Y A374241 Cf. A374239 (minimal), A374240 (maximal), A374242 (minimal nonzero absolute value).
%K A374241 nonn,hard,more
%O A374241 0,5
%A A374241 _Stefano Spezia_, Jul 01 2024
%E A374241 a(11)-a(14) from _Lucas A. Brown_, Oct 10 2024