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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 Table of n, a(n) for n=0..16. 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 Adjacent sequences: A358160 A358161 A358162 * A358164 A358165 A358166 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.)