A211147 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and nonnegative determinant.

1, 57, 377, 1345, 3553, 7737, 14937, 26177, 42945, 66681, 99193, 142209, 198241, 269049, 357593, 466433, 598401, 756281, 944057, 1164289, 1421601, 1719161, 2061081, 2451329, 2895489, 3396729, 3960569, 4591937, 5296289, 6077881

Offset: 0

Author

Clark Kimberling, Apr 03 2012

Keywords

• nonn

Comments

It appears that all terms are of the form 8*k + 1.

For a guide to related sequences, see A210000.

Crossrefs

Cf. A210000.

Programs

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, 0, m}]
Table[c1[n, 2 n^2], {n, 0, z1}]