A351147 - OEIS

%I #10 Aug 17 2023 08:16:46

%S 1,-7,-152,-6276,-550010,-94974369

%N a(n) is the minimal determinant of a symmetric n X n matrix using the integers 1 to n*(n+1)/2.

%e a(2) = -7:

%e   [1, 3;

%e    3, 2]

%e .

%e a(3) = -152:

%e   [5, 4, 1;

%e    4, 2, 6;

%e    1, 6, 3]

%e .

%e a(4) = -6276:

%e   [9,  5,  2,  4;

%e    5,  6, 10,  1;

%e    2, 10,  3,  7;

%e    4,  1,  7,  8]

%e .

%e a(5) = -550010:

%e   [ 3, 14,  7, 13,  9;

%e    14,  8,  1, 12,  4;

%e     7,  1,  6, 10, 15;

%e    13, 12, 10,  2, 11;

%e     9,  4, 15, 11,  5]

%e .

%e a(6) = -94974369:

%e   [ 5, 14,  7, 11, 21, 17;

%e    14, 12, 19,  3, 16,  1;

%e     7, 19, 13, 18,  2,  6;

%e    11,  3, 18, 10,  4, 20;

%e    21, 16,  2,  4,  9, 15;

%e    17,  1,  6, 20, 15,  8]

%Y Cf. A000217, A085000, A351148, A351609.

%K sign,hard,more

%O 1,2

%A _Hugo Pfoertner_ at the suggestion of _Markus Sigg_, Feb 15 2022