

A183761


Number of 2 X 2 nonsingular 0..n matrices with rows in increasing order.


2



3, 25, 96, 256, 563, 1073, 1880, 3056, 4715, 6961, 9944, 13752, 18603, 24601, 31936, 40800, 51427, 63937, 78664, 95720, 115435, 138057, 163888, 193064, 226059, 263089, 304480, 350528, 401715, 458145, 520488, 588872, 663803, 745681, 834872, 931736
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OFFSET

1,1


COMMENTS

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


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200


EXAMPLE

Some solutions for n=2:
..1..0....1..0....1..2....0..2....1..1....1..1....0..1....2..0....0..2....1..2
..2..2....1..2....2..1....1..0....2..0....1..2....2..0....2..1....1..2....2..2
Contribution from Clark Kimberling, Mar 19 2012: (Start)
As an example for counting positive determinants (see Comments), the 3 matrices counted by a(1) are
1 0.....1 1.....1 0
0 1.....0 1.....1 1 (End)


MATHEMATICA

a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w*z  x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
Table[c1[n, n^2]  c[n, 0], {n, 0, z1}]
(* Clark Kimberling, Mar 19 2012 *)


CROSSREFS

Sequence in context: A041565 A114378 A075306 * A212054 A180324 A124245
Adjacent sequences: A183758 A183759 A183760 * A183762 A183763 A183764


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 06 2011


STATUS

approved



