A358157 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3).

1, 0, 0, 1, 32, 1422, 146720, 18258864, 3217515264, 910849979232, 316878962588928, 143616562358849280, 90359341652805156864, 68004478547050644357120, 63187026071337208000512000, 75392341069747600992153600000, 104962910849766568886449582080000, 174017685915978467201007058206720000

Offset

0,5

Comments

The matrix M(n) is the n-th principal submatrix of the rectangular array A143974.

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

Links

Table of n, a(n) for n=0..17.

Example

a(5) = 1422:
    0  0  1  1  1
    0  1  2  2  3
    1  2  3  4  5
    1  2  4  5  6
    1  3  5  6  8

Mathematica

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

Prog

(Python)
from sympy import Matrix
def A358157(n): return Matrix(n, n, [i*j//3 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

Crossrefs

Cf. A143974.

Cf. A000212 (matrix element M[n,n]), A181286 (trace of M(n)), A358158 (hafnian of M(2*n)).

Sequence in context: A302806 A303467 A240345 * A300470 A326103 A300809

Adjacent sequences: A358154 A358155 A358156 * A358158 A358159 A358160

Keyword

nonn

Author

Stefano Spezia, Nov 01 2022

Status

approved