A086264 Number of real {0,1} n X n matrices having determinant=1.

1, 1, 3, 84, 10020, 4851360, 9240051240, 67745781734400, 1883481284085791040

Offset: 0

Author

Hugo Pfoertner, Oct 05 2003

Keywords

• nonn
• more

Links

• Hugo Pfoertner, Determinants of (0,1)-matrices. FORTRAN program.
• Minfeng Wang, C++ program
• Eric Weisstein's World of Mathematics, (0,1)-Matrix.
• Index entries for sequences related to binary matrices

Crossrefs

Cf. A003024, A003432, A051752, A055165.

Cf. A046747.

Programs

Mathematica

a[n_] := Module[{M, iter, cnt = 0}, M = Table[a[i, j], {i, 1, n}, {j, 1, n}]; iter = Thread[{Flatten[M], 0, 1}]; Do[If[Det[M] == 1, cnt++], Evaluate[Sequence @@ iter]]; cnt];
Do[Print[n, " ", a[n]], {n, 1, 4}] (* Jean-François Alcover, Dec 09 2018 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 18 2022

a(7) from Minfeng Wang, Feb 09 2023

a(8) from Minfeng Wang, Apr 26 2024