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A351020 Maximal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.

%I A351020 #21 Oct 13 2022 06:49:47
%S A351020 1,1,5,64,1650,66731,3968777,323676148,34890266414,4780256317586,
%T A351020 814873637329516,168491370685328792
%N A351020 Maximal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.
%H A351020 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A351019%2B20.sage">A351019+20.sage</a>
%H A351020 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A351020 a(3) = 64:
%e A351020      2    3    1
%e A351020      3    2    3
%e A351020      1    3    2
%e A351020 a(4) = 1650:
%e A351020      3    4    2    1
%e A351020      4    3    4    2
%e A351020      2    4    3    4
%e A351020      1    2    4    3
%e A351020 a(5) = 66731:
%e A351020      3    5    4    2    1
%e A351020      5    3    5    4    2
%e A351020      4    5    3    5    4
%e A351020      2    4    5    3    5
%e A351020      1    2    4    5    3
%o A351020 (Python)
%o A351020 from itertools import permutations
%o A351020 from sympy import Matrix
%o A351020 def A351020(n): return 1 if n == 0 else max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(range(1,n+1))) # _Chai Wah Wu_, Jan 31 2022
%Y A351020 Cf. A204235, A307783, A350938, A351019 (minimal).
%K A351020 nonn,hard,more
%O A351020 0,3
%A A351020 _Stefano Spezia_, Jan 29 2022
%E A351020 a(9) from _Alois P. Heinz_, Jan 31 2022
%E A351020 a(10)-a(11) from _Lucas A. Brown_, Sep 06 2022