A056989 Number of nonsingular n X n (-1,0,1)-matrices (over the reals).

1, 2, 48, 11808, 27947520, 609653621760

Offset

0,2

Comments

It would be nice to have an estimate for the asymptotic rate of growth.

Links

Table of n, a(n) for n=0..5.

Eric Weisstein's World of Mathematics, Nonsingular Matrix

Index entries for sequences related to binary matrices

Formula

a(n) = A060722(n) - A057981(n). - Alois P. Heinz, Dec 02 2019

Example

a(1) = 2: [1], [ -1].
a(2) = 48: There are 8 choices for the first column, u (say) and then the 2nd column can be anything except 0, u, -u, so 6 choices, giving a total of 8*6 = 48.

Mathematica

(* A brute force solution up to n = 4 *) a[n_] := a[n] = (m = Array[x, {n, n}]; cnt = 0; iter = {#, -1, 1}& /@ Flatten[m]; Do[ If[ Det[m] != 0, cnt++], Evaluate[ Sequence @@ iter]]; cnt); Table[ Print[a[n]]; a[n], {n, 1, 4}] (* Jean-François Alcover, Oct 11 2012 *)

Crossrefs

Cf. A055165, A053290, A056990, A055165, A002884, A046747, A057981, A060722.

Sequence in context: A002820 A196448 A053290 * A352207 A230886 A368132

Adjacent sequences: A056986 A056987 A056988 * A056990 A056991 A056992

Keyword

nonn,nice,more

Author

Eric W. Weisstein

Extensions

a(4) from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000

Entry revised by N. J. A. Sloane, Jan 02 2007

a(5) from Giovanni Resta, Feb 20 2009

a(0)=1 prepended by Alois P. Heinz, Dec 02 2019

Status

approved