A210290 Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative determinant.

1, 13, 56, 160, 369, 733, 1328, 2216, 3505, 5285, 7680, 10792, 14809, 19813, 26024, 33600, 42721, 53549, 66384, 81336, 98761, 118821, 141784, 167888, 197561, 230917, 268352, 310176, 356753, 408285, 465376, 528088, 597049, 672533, 754944, 844744, 942425

Offset: 0

Author

Clark Kimberling, Mar 19 2012

Keywords

• nonn

Comments

See A210000 for a guide to related sequences.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A059306, A210000.

Programs

Mathematica

a = 0; b = n; z1 = 45;
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], {n, 0, z1}]   (* A210290 *)

Formula

a(n) = ((n+1)^4 + A059306(n))/2. - Andrew Howroyd, Apr 28 2020

Extensions

Terms a(34) and beyond from Andrew Howroyd, Apr 28 2020