A350930 Minimal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.

1, 1, -5, -42, -1810, -48098, -2737409, -114381074

Offset: 0

Author

Stefano Spezia, Jan 25 2022

Keywords

• sign
• hard
• more

Examples

			a(2) = -5:
   [1    2]
   [3    1]
a(3) = -42:
   [3    4    1]
   [5    3    4]
   [2    5    3]
		

Links

• Lucas A. Brown, A350930+1.py
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A322908, A323254, A350931 (maximal).

Programs

Python

from itertools import permutations
from sympy import Matrix
def A350930(n): return min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022

Extensions

a(5) from Alois P. Heinz, Jan 25 2022

a(6) from Pontus von Brömssen, Jan 26 2022

a(7) from Lucas A. Brown, Aug 28 2022