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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). 2
1, 0, 1, 30, 1272, 113224, 18615680, 4299553536, 1507609286784, 781464165813504, 525599814806986752, 473934337123421786112, 567876971785035135320064, 837723761443461191423754240, 1549608938859438129393893376000, 3582000047767392376356107059200000, 9838495669776145718724862743674880000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
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.
LINKS
EXAMPLE
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
MATHEMATICA
a[n_]:=Permanent[Table[i*j-Ceiling[i*j/3], {i, n}, {j, n}]]; Join[{1}, Array[a, 16]]
PROG
(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
CROSSREFS
Cf. A143979.
Cf. A030511 (matrix element M[n-1,n-1]), A358164 (hafnian of M(2*n)).
Sequence in context: A163521 A273416 A002456 * A107768 A353104 A048536
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 01 2022
STATUS
approved

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Last modified February 26 20:11 EST 2024. Contains 370352 sequences. (Running on oeis4.)