A392338 - OEIS

%I #22 Jan 28 2026 01:22:16

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

%N 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].

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.

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

%e a(4) = 48:

%e   [3, 0, 2, 1]

%e   [1, 3, 0, 2]

%e   [2, 1, 3, 0]

%e   [0, 2, 1, 3]

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

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

%K nonn,hard,more

%O 2,2

%A _Stefano Spezia_, Jan 07 2026

%E a(10)-a(12) from _Hugo Pfoertner_, Jan 09 2026

%E a(13) from _Hugo Pfoertner_, Jan 12 2026