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.

1, 1, 0, 0, 40, 256, 12232, 526773, 8684025, 768561384, 28938090375, 1273675677456, 73821863714933, 7601760995500947, 527066887623562528

Offset

0,5

Links

Table of n, a(n) for n=0..14.

Lucas A. Brown, Python program.

Wikipedia, Toeplitz Matrix.

Example

a(5) = 256:
  [1, 4, 1, 2, 3]
  [4, 1, 4, 1, 2]
  [1, 4, 1, 4, 1]
  [2, 1, 4, 1, 4]
  [3, 2, 1, 4, 1]

Mathematica

a[0]=1; a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]

Crossrefs

Cf. A350954, A374139.

Cf. A374239 (minimal), A374241 (maximal absolute value), A374242 (minimal nonzero absolute value).

Sequence in context: A223426 A290127 A115170 * A247406 A229588 A334121

Adjacent sequences: A374237 A374238 A374239 * A374241 A374242 A374243

Keyword

nonn,hard,more

Author

Stefano Spezia, Jul 01 2024

Extensions

a(11)-a(14) from Lucas A. Brown, Oct 10 2024

Status

approved