A211057 Number of 2 X 2 matrices having all terms in {1,...,n} and determinant in the closed interval [0,n].

1, 10, 36, 91, 179, 330, 516, 802, 1150, 1615, 2119, 2873, 3595, 4558, 5653, 6967, 8245, 10020, 11642, 13846, 16053, 18524, 20944, 24393, 27405, 30924, 34637, 39035, 42961, 48396, 52906, 58687, 64326, 70457, 76722, 84824, 91318, 99045

Offset

1,2

Comments

For a guide to related sequences, see A210000.

Links

Table of n, a(n) for n=1..38.

Mathematica

a = 1; 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, 0, m}]
Table[c1[n, n], {n, 1, z1}]  (* A211057 *)

Crossrefs

Cf. A210000.

Sequence in context: A033585 A118629 A050509 * A118415 A051959 A117327

Adjacent sequences: A211054 A211055 A211056 * A211058 A211059 A211060

Keyword

nonn

Author

Clark Kimberling, Mar 31 2012

Status

approved