A211031 Number of 2 X 2 matrices having all elements in {0,1,...,n} and determinant in the closed interval [-n,n].

1, 16, 69, 176, 375, 650, 1107, 1626, 2413, 3326, 4527, 5782, 7689, 9436, 11753, 14354, 17491, 20458, 24623, 28334, 33425, 38438, 44031, 49450, 57323, 64028, 71849, 80078, 89857, 98468, 110545, 120388, 133117, 145382, 158699, 172256

Offset

0,2

Comments

For a guide to related sequences, see A210000.

Links

Table of n, a(n) for n=0..35.

Mathematica

a = 0; b = n; z1 = 40;
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, -n, m}]
Table[c1[n, n], {n, 0, z1}]  (* A211031 *)

Crossrefs

Cf. A210000, A211032.

Sequence in context: A299385 A299184 A299945 * A200839 A036660 A063493

Adjacent sequences: A211028 A211029 A211030 * A211032 A211033 A211034

Keyword

nonn

Author

_Clark Kimberling_, Mar 30 2012

Status

approved