A127186 Number of nonsingular n X n real {0,1}-matrices such that all upper left i X i submatrices are singular for i = 1..n-1.

1, 2, 40, 3936, 1695296

Offset: 1

Author

Artur Jasinski, Jan 08 2007

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A125587, A125593, A127182, A127183.

Programs

Mathematica

check[x_,n_] := Catch@ Block[{m = Partition[ IntegerDigits[x, 2, n^2], n]}, Do[ If[ Det[m[[1 ;; k, 1 ;; k]]] != 0, Throw@ False], {k, n-1}]; Det[m] != 0]; a[n_] := Length@ Parallelize@ Select[ Range[0, 2^(n^2) - 1], check[#, n] &]; Array[a, 4] (* Giovanni Resta, Jul 23 2025 *)

Extensions

a(1) and a(4) corrected by Giovanni Resta, Jul 23 2025