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a(n) is the maximal permanent of an n X n matrix using the integers 1 to n^2.
9

%I #10 Aug 17 2023 08:16:42

%S 1,1,14,947,161388,56558003,36757837732

%N a(n) is the maximal permanent of an n X n matrix using the integers 1 to n^2.

%e a(2) = 14:

%e [2, 3;

%e 4, 1]

%e .

%e a(3) = 947:

%e [3, 7, 6;

%e 9, 4, 1;

%e 2, 5, 8]

%e .

%e a(4) = 161388:

%e [ 2, 3, 16, 6;

%e 11, 13, 4, 10;

%e 8, 9, 5, 15;

%e 14, 12, 1, 7]

%e .

%e a(5) = 56558003:

%e [10, 2, 19, 25, 3;

%e 11, 5, 23, 20, 8;

%e 21, 14, 12, 9, 15;

%e 13, 24, 6, 1, 18;

%e 16, 17, 7, 4, 22]

%e .

%e a(6) = 36757837732:

%e [32, 30, 3, 19, 23, 2;

%e 1, 5, 34, 14, 11, 36;

%e 17, 18, 15, 31, 22, 16;

%e 29, 28, 7, 20, 24, 6;

%e 26, 25, 10, 21, 27, 9;

%e 4, 8, 35, 13, 12, 33]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A350566(n): return 1 if n == 0 else max(Matrix(n,n,p).per() for p in permutations(range(1,n**2+1))) # _Chai Wah Wu_, Jan 21 2022

%Y Cf. A085000, A350565, A350858, A350859.

%K nonn,hard,more

%O 0,3

%A _Hugo Pfoertner_ at the suggestion of _Stefano Spezia_, Jan 21 2022