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A056989
Number of nonsingular n X n (-1,0,1)-matrices (over the reals).
7
1, 2, 48, 11808, 27947520, 609653621760, 119288919620689920
OFFSET
0,2
COMMENTS
It would be nice to have an estimate for the asymptotic rate of growth.
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 *)
KEYWORD
nonn,nice,more
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