A211153 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and determinant >= 3n.

0, 20, 184, 804, 2284, 5408, 10780, 20084, 33664, 53840, 81124, 119156, 167872, 231096, 309816, 409128, 527088, 673112, 842776, 1049352, 1285760, 1561932, 1879908, 2247884, 2662000, 3134360, 3662256, 4264796, 4926892, 5673180

Offset

1,2

Comments

For a guide to related sequences, see A210000.

Links

Table of n, a(n) for n=1..30.

Mathematica

a = -n; 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, -2*n^2, m}]
Table[c1[n, 2*n^2]-c1[n, 3n-1], {n, 1, z1}] (* A211153 *)
%/4 (* integers *)

Crossrefs

Cf. A210000.

Sequence in context: A361609 A219581 A177073 * A210429 A367780 A047645

Adjacent sequences: A211150 A211151 A211152 * A211154 A211155 A211156

Keyword

nonn

Author

Clark Kimberling, Apr 05 2012

Status

approved