OFFSET
0,2
COMMENTS
It would be nice to have an estimate for the asymptotic rate of growth.
LINKS
Minfeng Wang, C++ program to calculate A056989
Eric Weisstein's World of Mathematics, Nonsingular Matrix
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}] (* Jean-François 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
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
a(0)-a(5) confirmed and a(6) added by Minfeng Wang, May 01 2024
STATUS
approved