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

0,2

Comments

See A210000 for a guide to related sequences.

Links

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

Formula

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

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 *)

Crossrefs

Cf. A059306, A210000.

Sequence in context: A061161 A212053 A264853 * A007202 A368813 A222161

Adjacent sequences: A210287 A210288 A210289 * A210291 A210292 A210293

Keyword

nonn

Author

Clark Kimberling, Mar 19 2012

Extensions

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

Status

approved