A211032 Number of 2 X 2 matrices having all elements in {0,1,...,n} and determinant in the open interval (-n,n).

10, 45, 134, 289, 560, 903, 1476, 2091, 3014, 4059, 5456, 6823, 8994, 10905, 13434, 16275, 19740, 22871, 27440, 31327, 36778, 42147, 48176, 53755, 62164, 69241, 77466, 86047, 96474, 105249, 118114, 128261, 141542, 154371, 168172

Offset

1,1

Comments

For a guide to related sequences, see A210000.

Links

Table of n, a(n) for n=1..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 - 1] - c1[n, -n], {n, 1, z1}] (* A211032 *)

Crossrefs

Cf. A210000, A211031.

Sequence in context: A226254 A340966 A022605 * A179095 A213188 A037270

Adjacent sequences: A211029 A211030 A211031 * A211033 A211034 A211035

Keyword

nonn

Author

Clark Kimberling, Mar 30 2012

Status

approved