|
%I #5 Jul 01 2024 19:21:55
%S 1,1,0,0,40,256,12232,526773,8684025,768561384,28938090375
%N 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e a(5) = 256:
%e [1, 4, 1, 2, 3]
%e [4, 1, 4, 1, 2]
%e [1, 4, 1, 4, 1]
%e [2, 1, 4, 1, 4]
%e [3, 2, 1, 4, 1]
%t 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 Cf. A350954, A374139.
%Y Cf. A374239 (minimal), A374241 (maximal absolute value), A374242 (minimal nonzero absolute value).
%K nonn,hard,more
%O 0,5
%A _Stefano Spezia_, Jul 01 2024
|
