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A374240 a(n) is the maximal 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 A374240 #9 Oct 10 2024 07:24:01
%S A374240 1,1,0,0,40,256,12232,526773,8684025,768561384,28938090375,
%T A374240 1273675677456,73821863714933,7601760995500947,527066887623562528
%N A374240 a(n) is the maximal 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 A374240 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A374239%2B40%2B41%2B42.py">Python program</a>.
%H A374240 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374240 a(5) = 256:
%e A374240   [1, 4, 1, 2, 3]
%e A374240   [4, 1, 4, 1, 2]
%e A374240   [1, 4, 1, 4, 1]
%e A374240   [2, 1, 4, 1, 4]
%e A374240   [3, 2, 1, 4, 1]
%t A374240 a[0]=1; a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
%Y A374240 Cf. A350954, A374139.
%Y A374240 Cf. A374239 (minimal), A374241 (maximal absolute value), A374242 (minimal nonzero absolute value).
%K A374240 nonn,hard,more
%O A374240 0,5
%A A374240 _Stefano Spezia_, Jul 01 2024
%E A374240 a(11)-a(14) from _Lucas A. Brown_, Oct 10 2024