A350931 - OEIS

%I #27 Dec 22 2023 16:37:09

%S 1,1,7,105,2294,71753,3051554,175457984

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

%C Also maximal absolute value of the determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1. - _Stefano Spezia_, Dec 22 2023

%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) = 7:

%e    [3    1]

%e    [2    3]

%e a(3) = 105:

%e    [5    1    3]

%e    [4    5    1]

%e    [2    4    5]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A350931(n): return max(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, A350930 (minimal).

%K nonn,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