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A358324
a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.
8
1, 0, 1, 8, 63, 2090, 36875, 1123653, 34292912, 1246207300, 53002204560, 2418538080316, 215120941720912
OFFSET
0,4
EXAMPLE
a(3) = 8:
[0, 2, 1;
2, 0, 2;
1, 2, 0]
a(4) = 63:
[1, 3, 2, 0;
3, 1, 3, 2;
2, 3, 1, 3;
0, 2, 3, 1]
a(5) = 2090:
[2, 4, 0, 1, 3;
4, 2, 4, 0, 1;
0, 4, 2, 4, 0;
1, 0, 4, 2, 4;
3, 1, 0, 4, 2]
MATHEMATICA
Join[{1}, Table[Max[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]], {i, n!}]], {n, 9}]]
CROSSREFS
Cf. A350954.
Cf. A358323 (minimal), A358325 (minimal nonzero absolute value), A358326 (minimal permanent), A358327 (maximal permanent).
Sequence in context: A361238 A353993 A189943 * A137664 A317028 A014392
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Nov 09 2022
EXTENSIONS
a(10)-a(12) from Lucas A. Brown, Nov 16 2022
STATUS
approved