A350954 - OEIS

%I #18 Oct 11 2022 00:55:00

%S 1,1,3,15,100,3091,49375,1479104,43413488,1539619328,64563673460,

%T 2877312739624,252631974548628

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

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A350953%2B4%2BA356865.py">A350953+4+A356865.py</a>

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

%e a(3) = 15:

%e     1    3    2

%e     3    1    3

%e     2    3    1

%e a(4) = 100:

%e     2    1    4    3

%e     1    2    1    4

%e     4    1    2    1

%e     3    4    1    2

%e a(5) = 3091:

%e     3    5    1    2    4

%e     5    3    5    1    2

%e     1    5    3    5    1

%e     2    1    5    3    5

%e     4    2    1    5    3

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A350954(n): return max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(range(1,n+1))) # _Chai Wah Wu_, Jan 27 2022

%Y Cf. A307887, A350931, A350953 (minimal), A356865 (minimal nonzero absolute value).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jan 27 2022

%E a(9) from _Alois P. Heinz_, Jan 27 2022

%E a(10)-a(12) from _Lucas A. Brown_, Sep 01 2022