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Maximal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.
9

%I #21 Oct 13 2022 06:49:47

%S 1,1,5,64,1650,66731,3968777,323676148,34890266414,4780256317586,

%T 814873637329516,168491370685328792

%N Maximal permanent 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/A351019%2B20.sage">A351019+20.sage</a>

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

%e a(3) = 64:

%e 2 3 1

%e 3 2 3

%e 1 3 2

%e a(4) = 1650:

%e 3 4 2 1

%e 4 3 4 2

%e 2 4 3 4

%e 1 2 4 3

%e a(5) = 66731:

%e 3 5 4 2 1

%e 5 3 5 4 2

%e 4 5 3 5 4

%e 2 4 5 3 5

%e 1 2 4 5 3

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o 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 Cf. A204235, A307783, A350938, A351019 (minimal).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jan 29 2022

%E a(9) from _Alois P. Heinz_, Jan 31 2022

%E a(10)-a(11) from _Lucas A. Brown_, Sep 06 2022