

A056989


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


6




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}] (* JeanFrançois Alcover, Oct 11 2012 *)


CROSSREFS

Cf. A055165, A053290, A056990, A055165, A002884, A046747, A057981, A060722.
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
a(0)=1 prepended by Alois P. Heinz, Dec 02 2019


STATUS

approved



