A392338 a(n) is the minimum absolute value of determinant of a nonsingular n X n circulant matrix whose rows are permutations of [0, 1, 2, ..., n-1].

1, 9, 48, 50, 2205, 147, 1120, 324, 5175, 605, 6336, 1014

Offset

2,2

Comments

The sequence has offset 2 since the only matrix of order 1 is [0] which is singular.

Links

Table of n, a(n) for n=2..13.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Wikipedia, Circulant matrix.

Formula

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

Example

a(4) = 48:
  [3, 0, 2, 1]
  [1, 3, 0, 2]
  [2, 1, 3, 0]
  [0, 2, 1, 3]

Crossrefs

Cf. A084367, A309257 (permutations of [1, 2, 3, ..., n]), A348891.

Cf. A392190 (max det), A392191 (min det), A392192 (max permanent), A392193 (min permanent).

Sequence in context: A293042 A159525 A173895 * A341757 A380964 A286437

Adjacent sequences: A392335 A392336 A392337 * A392339 A392340 A392342

Keyword

nonn,hard,more

Author

Stefano Spezia, Jan 07 2026

Extensions

a(10)-a(12) from Hugo Pfoertner, Jan 09 2026

a(13) from Hugo Pfoertner, Jan 12 2026

Status

approved