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A350954 Maximal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.

%I A350954 #18 Oct 11 2022 00:55:00
%S A350954 1,1,3,15,100,3091,49375,1479104,43413488,1539619328,64563673460,
%T A350954 2877312739624,252631974548628
%N A350954 Maximal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.
%H A350954 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A350953%2B4%2BA356865.py">A350953+4+A356865.py</a>
%H A350954 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A350954 a(3) = 15:
%e A350954     1    3    2
%e A350954     3    1    3
%e A350954     2    3    1
%e A350954 a(4) = 100:
%e A350954     2    1    4    3
%e A350954     1    2    1    4
%e A350954     4    1    2    1
%e A350954     3    4    1    2
%e A350954 a(5) = 3091:
%e A350954     3    5    1    2    4
%e A350954     5    3    5    1    2
%e A350954     1    5    3    5    1
%e A350954     2    1    5    3    5
%e A350954     4    2    1    5    3
%o A350954 (Python)
%o A350954 from itertools import permutations
%o A350954 from sympy import Matrix
%o A350954 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 A350954 Cf. A307887, A350931, A350953 (minimal), A356865 (minimal nonzero absolute value).
%K A350954 nonn,hard,more
%O A350954 0,3
%A A350954 _Stefano Spezia_, Jan 27 2022
%E A350954 a(9) from _Alois P. Heinz_, Jan 27 2022
%E A350954 a(10)-a(12) from _Lucas A. Brown_, Sep 01 2022