A086264 -id:A086264 - cp's OEIS frontend

A051752 Number of n X n (real) {0,1}-matrices having determinant A003432(n).

1, 1, 3, 3, 60, 3600, 529200, 75600, 195955200, 13716864000

Offset: 0

Eric Weisstein's World of Mathematics, Hadamard's Maximum Determinant Problem.
Eric Weisstein's World of Mathematics, (0, 1)-Matrix
Luke Zeng, Shawn Xin, Avadesian Xu, Thomas Pang, Tim Yang, Maolin Zheng, Seele's New Anti-ASIC Consensus Algorithm with Emphasis on Matrix Computation, arXiv:1905.04565 [cs.CR], 2019.
Miodrag Zivkovic, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005.
Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.

Cf. A003432, A046747, A086264, A089478, A188895.

a(5) = 3600 from Daniel P. Corson (danl(AT)MIT.EDU), Jan 09 2000
a(6) = 529200, a(7) = 75600 from Ulrich Hermisson (uhermiss(AT)rz.uni-leipzig.de), Feb 25 2003
More terms from Miodrag Zivkovic (ezivkovm(AT)matf.bg.ac.yu), Feb 28 2006
a(0)=1 prepended by Alois P. Heinz, Dec 20 2023

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

Hugo Pfoertner, Nov 04 2003

The first 4 rows were provided by Wouter Meeussen.

			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;
  ...

Minfeng Wang, Table of n, a(n) for n = 0..118

Cf. T(n,0) = A046747(n), T(n,1) = A086264(n), T(n,A003432(n)) = A051752(n).
The n-th row of the table contains A089472(n) nonzero entries.
Cf. A089479.

Fortran
```
c See link in A086264.
```

Edited by Alois P. Heinz, Dec 20 2023

A119008 Number of n X n real symmetric (0,1)-matrices with determinant = 1.

Original entry on oeis.org

1, 1, 4, 268, 9456, 301306, 24846368, 8946957244, 4175660906560, 2421067614753916

Offset: 1

Giovanni Resta, May 08 2006

Cf. A086264, A086899, A086900, A086906, A118998, A119002, A119009.

a(8)-a(10) from Max Alekseyev, Jun 17 2025

cp's OEIS Frontend

A051752 Number of n X n (real) {0,1}-matrices having determinant A003432(n).

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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).

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A119008 Number of n X n real symmetric (0,1)-matrices with determinant = 1.

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