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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)