A351022 Maximal permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 2, 13, 289, 13814, 1795898, 265709592, 70163924440, 20610999526800, 9097511018219760, 6845834489829830144

Offset: 0

Author

Stefano Spezia, Jan 29 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 289:
    3    5    2
    5    3    5
    2    5    3
a(4) = 13814:
    5    7    3    2
    7    5    7    3
    3    7    5    7
    2    3    7    5
a(5) = 1795898:
    5   11    7    3    2
   11    5   11    7    3
    7   11    5   11    7
    3    7   11    5   11
    2    3    7   11    5
		

Links

• Lucas A. Brown, A351021+2.sage
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A350940, A350956, A351021 (minimal).

Programs

Python

from itertools import permutations
from sympy import Matrix, prime
def A351022(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(prime(i) for i in range(1,n+1))) # Chai Wah Wu, Jan 31 2022

Extensions

a(9) and a(10) from Lucas A. Brown, Sep 04 2022