A209995 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant in {0,1,...,n}.

1, 13, 50, 120, 244, 410, 681, 981, 1431, 1948, 2623, 3315, 4373, 5323, 6588, 8009, 9706, 11290, 13535, 15503, 18233, 20912, 23879, 26725, 30910, 34443, 38556, 42887, 48041, 52519, 58888, 63994, 70647, 77056, 83981, 91064, 100373

Offset

0,2

Comments

See A210000 for a guide to related sequences.

Links

Table of n, a(n) for n=0..36.

Mathematica

a = 0; b = n; z1 = 40;
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}]   (* A209995 *)

Crossrefs

Cf. A210000.

Sequence in context: A189054 A231947 A322615 * A050410 A121991 A121990

Adjacent sequences: A209992 A209993 A209994 * A209996 A209997 A209998

Keyword

nonn

Author

Clark Kimberling, Mar 18 2012

Status

approved