A350937 Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.

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

Offset

0,3

Comments

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

Also minimal permanent of an n X n Hankel matrix using the integers 1 to 2*n - 1. - Stefano Spezia, Dec 22 2023

Links

Table of n, a(n) for n=0..7.

Lucas A. Brown, A350937+8.sage

Wikipedia, Toeplitz Matrix

Example

a(2) = 7:
    1    2
    3    1
a(3) = 89:
    1    2    4
    3    1    2
    5    3    1

Prog

(Python)
from itertools import permutations
from sympy import Matrix
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

Crossrefs

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

Sequence in context: A062747 A099719 A142995 * A200832 A103064 A244849

Adjacent sequences: A350934 A350935 A350936 * A350938 A350939 A350940

Keyword

nonn,hard,more

Author

Stefano Spezia, Jan 26 2022

Extensions

a(5) from Alois P. Heinz, Jan 26 2022

a(6) from Lucas A. Brown, Sep 04 2022

a(7) from Giovanni Resta, Oct 13 2022

Status

approved