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

0,2

Links

Table of n, a(n) for n=0..10.

Lucas A. Brown, A351021+2.sage

Wikipedia, Toeplitz Matrix

Example

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

Prog

(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

Crossrefs

Cf. A350940, A350956, A351021 (minimal).

Sequence in context: A123113 A126742 A013051 * A012955 A357342 A011808

Adjacent sequences: A351019 A351020 A351021 * A351023 A351024 A351025

Keyword

nonn,hard,more

Author

Stefano Spezia, Jan 29 2022

Extensions

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

Status

approved