A369835 - OEIS

A369835

a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the integers 0 to n-1.

%I #11 Feb 11 2024 11:28:44

%S 1,1,1,6,23,119,718,5038,40320,362879

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

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

%F a(n) <= A000142(n).

%t a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A369835(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(range(n))}) # _Chai Wah Wu_, Feb 11 2024

%Y Cf. A000142, A358326, A358327.

%Y Cf. A369830, A369831, A369832, A369833, A369834.

%K nonn,hard,more

%O 0,4

%A _Stefano Spezia_, Feb 03 2024