A351019 Minimal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.

1, 1, 5, 36, 480, 9991, 296913, 12099604, 637590728, 43090005714, 3550491371994, 359557627057876

Offset: 0

Author

Stefano Spezia, Jan 29 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 36:
    2    1    3
    1    2    1
    3    1    2
a(4) = 480:
    2    1    3    4
    1    2    1    3
    3    1    2    1
    4    3    1    2
a(5) = 9991:
    3    1    2    4    5
    1    3    1    2    4
    2    1    3    1    2
    4    2    1    3    1
    5    4    2    1    3
		

Links

• Lucas A. Brown, A351019+20.sage
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A204235, A307783, A350937, A351020 (maximal).

Programs

Python

from itertools import permutations
from sympy import Matrix
def A351019(n): return 1 if n == 0 else min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(range(1,n+1))) # Chai Wah Wu, Jan 31 2022

Extensions

a(9) from Alois P. Heinz, Jan 31 2022

a(10)-a(11) from Lucas A. Brown, Sep 06 2022