login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056989 Number of nonsingular n X n (-1,0,1)-matrices (over the reals). 6
2, 48, 11808, 27947520, 609653621760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..5.

Eric Weisstein's World of Mathematics, Nonsingular Matrix

Index entries for sequences related to binary matrices

FORMULA

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

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-Fran├žois Alcover, Oct 11 2012 *)

CROSSREFS

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

Sequence in context: A002820 A196448 A053290 * A230886 A090770 A081960

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)