A392187 - OEIS

%I #22 Jan 05 2026 15:15:58

%S 1,1,-3,18,-160,75,-41895,196,-26978400,0,-36843728625,726,

%T -89802671542272,1183,-354379732734283200

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

%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 a(n) = - A328030(n) for n even.

%e a(4) = -160:

%e   [3, 2, 1, 4]

%e   [4, 3, 2, 1]

%e   [1, 4, 3, 2]

%e   [2, 1, 4, 3]

%Y Cf. A328030 (max det), A392188 (max permanent), A392189 (min permanent).

%Y Cf. A309257, A392131, A392191.

%K sign,hard,more

%O 0,3

%A _Stefano Spezia_, Jan 03 2026

%E a(11)-a(14) from _Hugo Pfoertner_, Jan 05 2026