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%I #16 Dec 02 2019 10:50:01
%S 1,2,48,11808,27947520,609653621760
%N Number of nonsingular n X n (-1,0,1)-matrices (over the reals).
%C It would be nice to have an estimate for the asymptotic rate of growth.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NonsingularMatrix.html">Nonsingular Matrix</a>
%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F a(n) = A060722(n) - A057981(n). - _Alois P. Heinz_, Dec 02 2019
%e a(1) = 2: [1], [ -1].
%e 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.
%t (* 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 *)
%Y Cf. A055165, A053290, A056990, A055165, A002884, A046747, A057981, A060722.
%K nonn,nice,more
%O 0,2
%A _Eric W. Weisstein_
%E a(4) from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000
%E Entry revised by _N. J. A. Sloane_, Jan 02 2007
%E a(5) from _Giovanni Resta_, Feb 20 2009
%E a(0)=1 prepended by _Alois P. Heinz_, Dec 02 2019
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