A358327 - OEIS

%I #10 Nov 16 2022 09:41:24

%S 1,0,1,12,304,12696,778785,64118596,7014698888,965862895732,

%T 166105870928994,34460169208369298

%N a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A358326%2B7.sage">A358326+7.sage</a>.

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

%e a(3) = 12:

%e     [2, 1, 0;

%e      1, 2, 1;

%e      0, 1, 2]

%e a(4) = 304:

%e     [2, 3, 1, 0;

%e      3, 2, 3, 1;

%e      1, 3, 2, 3;

%e      0, 1, 3, 2]

%e a(5) = 12696:

%e     [3, 4, 2, 1, 0;

%e      4, 3, 4, 2, 1;

%e      2, 4, 3, 4, 2;

%e      1, 2, 4, 3, 4;

%e      0, 1, 2, 4, 3]

%t Join[{1}, Table[Max[Table[Permanent[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]],{i,n!}]],{n,9}]]

%Y Cf. A351020.

%Y Cf. A358323 (minimal determinant), A358324 (maximal determinant), A358326 (minimal).

%K nonn,hard,more

%O 0,4

%A _Stefano Spezia_, Nov 09 2022

%E a(10) and a(11) from _Lucas A. Brown_, Nov 16 2022