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A211146
Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and 0 <= determinant <= n.
2
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 03 2012
EXTENSIONS
Offset changed to 0 by Georg Fischer, Feb 02 2022
STATUS
approved