A350937 - OEIS

%I #31 Dec 22 2023 16:35:54

%S 1,1,7,89,2287,89025,5141775,404316249

%N Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.

%C At least up to a(7) the minimal permanent is attained by a matrix which has 1, 3, 5, ... as first row and 1, 2, 4, 6,... as first column. - _Giovanni Resta_, Oct 13 2022

%C Also minimal permanent of an n X n Hankel matrix using the integers 1 to 2*n - 1. - _Stefano Spezia_, Dec 22 2023

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A350937%2B8.sage">A350937+8.sage</a>

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

%e a(2) = 7:

%e     1    2

%e     3    1

%e a(3) = 89:

%e     1    2    4

%e     3    1    2

%e     5    3    1

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A350937(n): return 1 if n == 0 else min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(range(1,2*n))) # _Chai Wah Wu_, Jan 27 2022

%Y Cf. A322908, A323254, A350930, A350938 (maximal).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jan 26 2022

%E a(5) from _Alois P. Heinz_, Jan 26 2022

%E a(6) from _Lucas A. Brown_, Sep 04 2022

%E a(7) from _Giovanni Resta_, Oct 13 2022