

A056989


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


7




OFFSET

0,2


COMMENTS

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


LINKS



FORMULA



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



KEYWORD

nonn,nice,more


AUTHOR



EXTENSIONS

a(4) from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000
a(0)a(5) confirmed and a(6) added by Minfeng Wang, May 01 2024


STATUS

approved



