A392191 a(n) is the minimum determinant of an n X n circulant matrix whose rows are permutations of [0, 1, 2, ..., n-1].

1, 0, -1, 9, -96, 50, -29925, 147, -20983200, 0, -30144868875, 605

Offset

0,4

Links

Table of n, a(n) for n=0..11.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Wikipedia, Circulant matrix.

Formula

a(n) = - A392190(n) for n even.

Conjecture: a(n) = A084367((n-1)/2) for n odd.

Example

a(4) = -96:
  [2, 1, 0, 3]
  [3, 2, 1, 0]
  [0, 3, 2, 1]
  [1, 0, 3, 2]

Crossrefs

Cf. A392190 (max det), A392192 (max permanent), A392193 (min permanent).

Cf. A084367, A392131, A392188.

Sequence in context: A065456 A052389 A197665 * A064504 A090448 A264219

Adjacent sequences: A392188 A392189 A392190 * A392192 A392193 A392194

Keyword

sign,hard,more

Author

Stefano Spezia, Jan 03 2026

Extensions

a(10)-a(11) from Hugo Pfoertner, Jan 04 2026

Status

approved