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%I #23 Oct 13 2022 06:50:26
%S 1,1,5,36,480,9991,296913,12099604,637590728,43090005714,
%T 3550491371994,359557627057876
%N Minimal 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) = 36:
%e 2 1 3
%e 1 2 1
%e 3 1 2
%e a(4) = 480:
%e 2 1 3 4
%e 1 2 1 3
%e 3 1 2 1
%e 4 3 1 2
%e a(5) = 9991:
%e 3 1 2 4 5
%e 1 3 1 2 4
%e 2 1 3 1 2
%e 4 2 1 3 1
%e 5 4 2 1 3
%o (Python)
%o from itertools import permutations
%o from sympy import Matrix
%o def A351019(n): return 1 if n == 0 else min(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, A350937, A351020 (maximal).
%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