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Minimal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
6

%I #24 Oct 11 2022 00:54:11

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

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

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A350930%2B1.py">A350930+1.py</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>

%e a(2) = -5:

%e [1 2]

%e [3 1]

%e a(3) = -42:

%e [3 4 1]

%e [5 3 4]

%e [2 5 3]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o 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

%Y Cf. A322908, A323254, A350931 (maximal).

%K sign,hard,more

%O 0,3

%A _Stefano Spezia_, Jan 25 2022

%E a(5) from _Alois P. Heinz_, Jan 25 2022

%E a(6) from _Pontus von Brömssen_, Jan 26 2022

%E a(7) from _Lucas A. Brown_, Aug 28 2022