A350566 a(n) is the maximal permanent of an n X n matrix using the integers 1 to n^2.

1, 1, 14, 947, 161388, 56558003, 36757837732

Offset

0,3

Links

Table of n, a(n) for n=0..6.

Example

a(2) = 14:
  [2, 3;
   4, 1]
.
a(3) = 947:
  [3, 7, 6;
   9, 4, 1;
   2, 5, 8]
.
a(4) = 161388:
  [ 2,  3, 16,  6;
   11, 13,  4, 10;
    8,  9,  5, 15;
   14, 12,  1,  7]
.
a(5) = 56558003:
  [10,  2, 19, 25,  3;
   11,  5, 23, 20,  8;
   21, 14, 12,  9, 15;
   13, 24,  6,  1, 18;
   16, 17,  7,  4, 22]
.
a(6) = 36757837732:
  [32, 30,  3, 19, 23,  2;
    1,  5, 34, 14, 11, 36;
   17, 18, 15, 31, 22, 16;
   29, 28,  7, 20, 24,  6;
   26, 25, 10, 21, 27,  9;
    4,  8, 35, 13, 12, 33]

Prog

(Python)
from itertools import permutations
from sympy import Matrix
def A350566(n): return 1 if n == 0 else max(Matrix(n, n, p).per() for p in permutations(range(1, n**2+1))) # Chai Wah Wu, Jan 21 2022

Crossrefs

Cf. A085000, A350565, A350858, A350859.

Sequence in context: A115458 A241801 A337576 * A199651 A241110 A055152

Adjacent sequences: A350563 A350564 A350565 * A350567 A350568 A350569

Keyword

nonn,hard,more

Author

Hugo Pfoertner at the suggestion of Stefano Spezia, Jan 21 2022

Status

approved