This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056989 #24 Feb 16 2025 08:32:43
%S A056989 1,2,48,11808,27947520,609653621760,119288919620689920
%N A056989 Number of nonsingular n X n (-1,0,1)-matrices (over the reals).
%C A056989 It would be nice to have an estimate for the asymptotic rate of growth.
%H A056989 Minfeng Wang, <a href="/A056989/a056989.cpp.txt">C++ program to calculate A056989</a>
%H A056989 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonsingularMatrix.html">Nonsingular Matrix</a>
%H A056989 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F A056989 a(n) = A060722(n) - A057981(n). - _Alois P. Heinz_, Dec 02 2019
%e A056989 a(1) = 2: [1], [ -1].
%e A056989 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 A056989 (* 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 A056989 Cf. A055165, A053290, A056990, A055165, A002884, A046747, A057981, A060722.
%K A056989 nonn,nice,more
%O A056989 0,2
%A A056989 _Eric W. Weisstein_
%E A056989 a(4) from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000
%E A056989 Entry revised by _N. J. A. Sloane_, Jan 02 2007
%E A056989 a(5) from _Giovanni Resta_, Feb 20 2009
%E A056989 a(0)=1 prepended by _Alois P. Heinz_, Dec 02 2019
%E A056989 a(0)-a(5) confirmed and a(6) added by _Minfeng Wang_, May 01 2024