A210368 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant >= 3n.

1, 0, 0, 7, 35, 104, 252, 509, 997, 1688, 2751, 4175, 6240, 8872, 12324, 16639, 22196, 28668, 36931, 46332, 58184, 71524, 87183, 105334, 126524, 150233, 177448, 207751, 242948, 281139, 324739

Offset: 0

Author

Clark Kimberling, Mar 20 2012

Keywords

• nonn

Comments

See A210000 for a guide to related sequences.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A210000.

Programs

Mathematica

a = 0; b = n; z1 = 30;
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] - c1[n, 3 n - 1], {n, 0, z1}]