A211146 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and 0 <= determinant <= n.

1, 53, 273, 737, 1613, 2821, 4853, 7125, 10593, 14597, 19885, 25309, 33677, 41189, 51269, 62565, 76145, 88793, 106821, 122581, 144541, 166045, 189997, 212877, 246653, 275081, 308369, 343281, 384977, 421097, 472649, 513865, 567765

Offset

0,2

Comments

For a guide to related sequences, see A210000.

Links

Table of n, a(n) for n=0..32.

Mathematica

a = -n; 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], {n, 0, z1}]              (* A211146 *)
(1/4) (-1 + Table[c1[n, n], {n, 0, z1}]) (* integers *)

Crossrefs

Cf. A210000.

Sequence in context: A337428 A253119 A253112 * A155700 A108878 A096325

Adjacent sequences: A211143 A211144 A211145 * A211147 A211148 A211149

Keyword

nonn

Author

Clark Kimberling, Apr 03 2012

Extensions

Offset changed to 0 by Georg Fischer, Feb 02 2022

Status

approved