A210367 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant >= 2n.

1, 0, 5, 26, 83, 203, 456, 853, 1497, 2477, 3860, 5690, 8305, 11470, 15684, 20947, 27328, 35057, 44569, 55569, 68849, 84153, 101912, 122125, 146014, 172246, 202378, 236593, 274399, 316494, 364473, 416055, 473938, 537432, 607225, 683593, 767218, 857111, 955830

Offset: 0

Author

Clark Kimberling, Mar 20 2012

Keywords

• nonn

Comments

See A210000 for a guide to related sequences.

Examples

			a(2)=5 counts these matrices:
  2 0...2 1...2 0...2 0...2 2
  0 2...0 2...1 2...2 2...0 2
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A210000.

Programs

Mathematica

a = 0; b = n; z1 = 20;
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, 2 n - 1], {n, 0, z1}]