A089478
Triangle T(n,k) read by rows, where T(n,k) = number of times the determinant of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= A003432(n).
Original entry on oeis.org
0, 1, 1, 1, 10, 3, 338, 84, 3, 42976, 10020, 1200, 60, 21040112, 4851360, 1213920, 144720, 43560, 3600, 39882864736, 9240051240, 3868663680, 768723480, 418703040, 63612360, 46569600, 6438600, 5014800, 529200, 292604283435872
Offset: 0
a(4) = T(2,1) = 3 because there are 3 different (0,1)-matrices with determinant=1:
((1,0),(0,1)), ((1,1),(0,1)), ((1,0),(1,1)).
Triangle T(n,k) begins:
0, 1;
1, 1;
10, 3;
338, 84, 3;
42976, 10020, 1200, 60;
21040112, 4851360, 1213920, 144720, 43560, 3600;
...
The n-th row of the table contains
A089472(n) nonzero entries.
A136609
(1/(n!)^2) * number of ways to arrange the consecutive numbers 1...n^2 in an n X n matrix with determinant = 0.
Original entry on oeis.org
0, 0, 76, 14392910
Offset: 1
a(1)=0 because det((1))/=0, a(2)=0, because the only possible determinants of a matrix with elements {1,2,3,4} are +-2, +-5 and +-10.
A057982
Number of singular n X n (-1,1)-matrices.
Original entry on oeis.org
0, 8, 320, 43264, 22003712, 43090149376, 326720427917312, 9588057159626653696, 1086099857128493963804672
Offset: 1
More terms from Kevin Costello, May 18 2005
a(6)-a(9) from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 18 2008
A116977
Number of n X n rational {0,1}-matrices of determinant 0, up to row and column permutations.
Original entry on oeis.org
1, 5, 28, 256, 4471, 187300, 22290203, 8267860926
Offset: 1
A192892
Number of n X n binary matrices whose determinants equal their permanents.
Original entry on oeis.org
1, 2, 12, 343, 34997, 12515441, 15749457081, 72424550598849, 1282759836215548737
Offset: 0
a(2) equals 12 because there are exactly twelve 2 X 2 binary matrices whose determinants equal their permanents; these matrices are:
|0 0| |1 0| |0 1| |1 1| |0 0| |1 0| |0 0| |1 0|
|0 0| |0 0| |0 0| |0 0| |1 0| |1 0| |0 1| |0 1|
.
|0 1| |1 1| |0 0| |1 0|
|0 1| |0 1| |1 1| |1 1|
-
Sum[KroneckerDelta[Det[Array[Mod[Floor[k/(2^(n*(#1 - 1) + #2 - 1))], 2] &, {n, n}]], Permanent[Array[Mod[Floor[k/(2^(n*(#1 - 1) + #2 - 1))], 2] &, {n, n}]]], {k, 0, (2^(n^2)) - 1}]
-
from itertools import product
from sympy import Matrix
def A192892(n): return 1 if n == 0 else sum(1 for m in product([0,1],repeat=n**2) if (lambda x:x.det()==x.per())(Matrix(n,n,m))) # Chai Wah Wu, Oct 01 2021
Definition and example slightly modified by
Harvey P. Dale, Feb 24 2017
Original entry on oeis.org
0, 0, 6, 431, 66056, 27960727, 35744362616, 144901919316449
Offset: 1
a(8) = 0 + 0 + 6 + 425 + 65625 + 27894671 + 35716401889 + 144866174953833.
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