A351020 Maximal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.

1, 1, 5, 64, 1650, 66731, 3968777, 323676148, 34890266414, 4780256317586, 814873637329516, 168491370685328792

Offset: 0

Author

Stefano Spezia, Jan 29 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 64:
     2    3    1
     3    2    3
     1    3    2
a(4) = 1650:
     3    4    2    1
     4    3    4    2
     2    4    3    4
     1    2    4    3
a(5) = 66731:
     3    5    4    2    1
     5    3    5    4    2
     4    5    3    5    4
     2    4    5    3    5
     1    2    4    5    3
		

Links

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

Crossrefs

Cf. A204235, A307783, A350938, A351019 (minimal).

Programs

Python

from itertools import permutations
from sympy import Matrix
def A351020(n): return 1 if n == 0 else max(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