A358163 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - ceiling(i*j/3).

1, 0, 1, 30, 1272, 113224, 18615680, 4299553536, 1507609286784, 781464165813504, 525599814806986752, 473934337123421786112, 567876971785035135320064, 837723761443461191423754240, 1549608938859438129393893376000, 3582000047767392376356107059200000, 9838495669776145718724862743674880000

Offset: 0

Author

Stefano Spezia, Nov 01 2022

Keywords

• nonn

Comments

The matrix M(n) is the n-th principal submatrix of the rectangular array A143979.

det(M(0)) = 1, det(M(2)) = -1, det(M(3)) = 2, and otherwise det(M(n)) = 0.

Examples

			a(5) = 113224:
    0  1   2   2   3
    1  2   4   5   6
    2  4   6   8  10
    2  5   8  10  13
    3  6  10  13  16
		

Crossrefs

Cf. A143979.

Cf. A030511 (matrix element M[n-1,n-1]), A358164 (hafnian of M(2*n)).

Programs

Mathematica

a[n_]:=Permanent[Table[i*j-Ceiling[i*j/3],{i,n},{j,n}]]; Join[{1},Array[a,16]]

Python

from fractions import Fraction
from sympy import Matrix
def A358163(n): return Matrix(n,n,[i*j-Fraction(i*j,3)._ceil_() for i in range(1,n+1) for j in range(1,n+1)]).per() if n else 1 # Chai Wah Wu, Nov 02 2022