A211059 Number of 2 X 2 matrices having all terms in {1,...,n} and positive determinant.

0, 5, 33, 112, 288, 605, 1145, 1968, 3176, 4861, 7161, 10152, 14040, 18917, 24961, 32352, 41312, 51949, 64585, 79320, 96472, 116277, 139025, 164840, 194184, 227261, 264385, 305840, 352096, 403245, 459945, 522312, 590840, 665917

Offset: 1

Author

Clark Kimberling, Mar 31 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A210000.

Crossrefs

Cf. A210000, A211056.

Programs

Mathematica

a = 1; b = n; z1 = 35;
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] - c[n, 0], {n, 1, z1}]   (* A211059 *)
2*%     (* A211056 *)