A183761 Number of 2 X 2 nonsingular 0..n matrices with rows in increasing order.

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

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