A374140 a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals abs(i-j) or 1 if i = j.

1, 1, 2, 11, 117, 2083, 55482, 2063149, 102176977, 6490667261, 514651043730, 49787897503031, 5771746960693493, 789652404867861919, 125885777192807718730, 23129357587464094132601, 4851600400570400272371009, 1152232847579194480216644249, 307579355879152834353840187554

Offset

0,3

Comments

Conjecture: a(n) is the minimal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal. - Stefano Spezia, Jul 05 2024

Links

Table of n, a(n) for n=0..18.

Example

a(4) = 117:
  [1, 1, 2, 3]
  [1, 1, 1, 2]
  [2, 1, 1, 1]
  [3, 2, 1, 1]

Mathematica

a[n_]:=Permanent[Table[If[i == j, 1, Abs[i - j]], {i, n}, {j, n}]]; Join[{1}, Array[a, 18]]

Prog

(PARI) a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 1, abs(i-j)))); \\ Michel Marcus, Jun 29 2024
(Python)
from sympy import Matrix
def A374140(n): return Matrix(n, n, [abs(j-k) if j!=k else 1 for j in range(n) for k in range(n)]).per() if n else 1 # Chai Wah Wu, Jul 01 2024

Crossrefs

Cf. A085807, A374067, A374139 (determinant).

Sequence in context: A181168 A269082 A304639 * A130222 A197993 A057076

Adjacent sequences: A374137 A374138 A374139 * A374141 A374142 A374143

Keyword

nonn

Author

Stefano Spezia, Jun 28 2024

Status

approved