A351147 a(n) is the minimal determinant of a symmetric n X n matrix using the integers 1 to n*(n+1)/2.

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

Offset: 1

Author

Hugo Pfoertner at the suggestion of Markus Sigg, Feb 15 2022

Keywords

• sign
• hard
• more

Examples

			a(2) = -7:
  [1, 3;
   3, 2]
.
a(3) = -152:
  [5, 4, 1;
   4, 2, 6;
   1, 6, 3]
.
a(4) = -6276:
  [9,  5,  2,  4;
   5,  6, 10,  1;
   2, 10,  3,  7;
   4,  1,  7,  8]
.
a(5) = -550010:
  [ 3, 14,  7, 13,  9;
   14,  8,  1, 12,  4;
    7,  1,  6, 10, 15;
   13, 12, 10,  2, 11;
    9,  4, 15, 11,  5]
.
a(6) = -94974369:
  [ 5, 14,  7, 11, 21, 17;
   14, 12, 19,  3, 16,  1;
    7, 19, 13, 18,  2,  6;
   11,  3, 18, 10,  4, 20;
   21, 16,  2,  4,  9, 15;
   17,  1,  6, 20, 15,  8]
		

Crossrefs

Cf. A000217, A085000, A351148, A351609.