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A374388 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 first n-1 primes off-diagonal.

%I A374388 #8 Jul 12 2024 12:02:59
%S A374388 1,0,4,36,324,15164,2287607,162104000,37905894000,4059346088384,
%T A374388 718058901423168,221630954408019520
%N A374388 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 first n-1 primes off-diagonal.
%H A374388 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%F A374388 a(n) = max(abs(A374386(n)), A374387(n)).
%e A374388 a(5) = 15164:
%e A374388   [0, 2, 7, 3, 5]
%e A374388   [2, 0, 2, 7, 3]
%e A374388   [7, 2, 0, 2, 7]
%e A374388   [3, 7, 2, 0, 2]
%e A374388   [5, 3, 7, 2, 0]
%t A374388 a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
%Y A374388 Cf. A071079, A374342.
%Y A374388 Cf. A374386 (minimal), A374387 (maximal), A374389 (minimal nonzero absolute value).
%Y A374388 Cf. A374068 (minimal permanent), A374390 (maximal permanent).
%K A374388 nonn,hard,more
%O A374388 0,3
%A A374388 _Stefano Spezia_, Jul 07 2024
%E A374388 a(11) from _Giorgos Kalogeropoulos_, Jul 12 2024