VOOZH about

URL: https://oeis.org/A358161

⇱ A358161 - OEIS

login
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).
2
1, 1, 3, 19, 434, 18142, 1138592, 131646240, 22247821152, 4990553682336, 1661493079305216, 729074911776673536, 397903630707426852864, 290086114501734871449600, 262660633302518916820992000, 284075108357948520100761600000, 385808192325346588875691868160000, 626209817056857125529475382231040000
OFFSET
0,3
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.
EXAMPLE
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
MATHEMATICA
a[n_]:=Permanent[Table[Ceiling[i j/3], {i, n}, {j, n}]]; Join[{1}, Array[a, 17]]
PROG
(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
CROSSREFS
Cf. A143977.
Cf. A008810 (matrix element M[n,n]), A070333 (trace of M(n+1)), A358162 (hafnian of M(2*n)).
Sequence in context: A365362 A143762 A228149 * A079281 A176232 A079306
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 01 2022
STATUS
approved