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A350937
Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
9
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
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
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