A358161 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3).

1, 1, 3, 19, 434, 18142, 1138592, 131646240, 22247821152, 4990553682336, 1661493079305216, 729074911776673536, 397903630707426852864, 290086114501734871449600, 262660633302518916820992000, 284075108357948520100761600000, 385808192325346588875691868160000, 626209817056857125529475382231040000

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 A143977.

det(M(n)) = 1 for n <= 3, and otherwise det(M(n)) = 0.

Examples

			a(5) = 18142:
    1  1  1  2  2
    1  2  2  3  4
    1  2  3  4  5
    2  3  4  6  7
    2  4  5  7  9
		

Crossrefs

Cf. A143977.

Cf. A008810 (matrix element M[n,n]), A070333 (trace of M(n+1)), A358162 (hafnian of M(2*n)).

Programs

Mathematica

a[n_]:=Permanent[Table[Ceiling[i j/3],{i,n},{j,n}]]; Join[{1},Array[a,17]]

Python

from fractions import Fraction
from sympy import Matrix
def A358161(n): return Matrix(n,n,[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