|
%I #14 Jul 07 2024 05:49:13
%S 1,0,1,8,256,9978,600052,49036950,5286564352,725724599636
%N a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e a(5) = 9978:
%e [0, 4, 3, 2, 1]
%e [4, 0, 4, 3, 2]
%e [3, 4, 0, 4, 3]
%e [2, 3, 4, 0, 4]
%e [1, 2, 3, 4, 0]
%t a[0]=1; a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
%Y Cf. A085807 (minimal), A358327.
%Y Cf. A374279, A374280, A374281, A374282.
%K nonn,hard,more
%O 0,4
%A _Stefano Spezia_, Jul 02 2024
|
