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%I #14 Jan 12 2017 01:47:28
%S 3,25,96,256,563,1073,1880,3056,4715,6961,9944,13752,18603,24601,
%T 31936,40800,51427,63937,78664,95720,115435,138057,163888,193064,
%U 226059,263089,304480,350528,401715,458145,520488,588872,663803,745681,834872,931736
%N Number of 2 X 2 nonsingular 0..n matrices with rows in increasing order.
%C Possibly this sequence gives the number of 2 X 2 matrices with all terms in {0,1,...,n} and positive determinant, as evidenced by a program in the Mathematica section. - _Clark Kimberling_, Mar 19 2012
%H R. H. Hardin, <a href="/A183761/b183761.txt">Table of n, a(n) for n = 1..200</a>
%e Some solutions for n=2:
%e ..1..0....1..0....1..2....0..2....1..1....1..1....0..1....2..0....0..2....1..2
%e ..2..2....1..2....2..1....1..0....2..0....1..2....2..0....2..1....1..2....2..2
%e Contribution from _Clark Kimberling_, Mar 19 2012: (Start)
%e As an example for counting positive determinants (see Comments), the 3 matrices counted by a(1) are
%e 1 0.....1 1.....1 0
%e 0 1.....0 1.....1 1 (End)
%t a = 0; b = n; z1 = 45;
%t t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t c[n_, k_] := c[n, k] = Count[t[n], k]
%t c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
%t Table[c1[n, n^2] - c[n, 0], {n, 0, z1}]
%t (* _Clark Kimberling_, Mar 19 2012 *)
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 06 2011
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