A359562 a(n) is the permanent of an n X n Hermitian Toeplitz matrix whose first row consists of n, (n-1)*i, (n-2)*i, ..., 3*i, 2*i, i, where i denotes the imaginary unit.

1, 1, 5, 54, 980, 26000, 977844, 48486480, 3168454720, 257625275760, 26347709832000, 3217348801257888, 477582176242255104, 82066363639286366080, 16709994767104962690304, 3847766849105116759200000, 1029727509567022262979280896, 306114655769763238348323419392, 104188715467117934409088054935552

Offset

0,3

Links

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

Wikipedia, Toeplitz Matrix

Formula

A359616(n) <= a(n) <= A359617(n).

Example

a(3) = 54:
  [   3,  2*i,   i;
   -2*i,    3, 2*i;
     -i, -2*i,   3 ]

Mathematica

Join[{1}, Table[Permanent[ToeplitzMatrix[Join[{n}, I Reverse[Range[n-1]]]]], {n, 18}]]

Prog

(Python)
from sympy import Matrix, I
def A359562(n): return Matrix(n, n, [(n+j-i if i>j else j-i-n) if i!=j else n*I for i in range(n) for j in range(n)]).per()*(1, -I, -1, I)[n&3] if n else 1 # Chai Wah Wu, Jan 25 2023

Crossrefs

Cf. A307783 (symmetric Toeplitz matrix).

Cf. A359559, A359560, A359561 (determinant).

Cf. A359616 (minimal), A359617 (maximal).

Sequence in context: A304322 A132619 A251583 * A359617 A223896 A245765

Adjacent sequences: A359559 A359560 A359561 * A359563 A359564 A359565

Keyword

nonn

Author

Stefano Spezia, Jan 06 2023

Status

approved