A209994 Number of 2 X 2 matrices with all elements in {1,2,...,n} and determinant in {-1,0,1}.

0, 1, 10, 31, 60, 105, 154, 223, 300, 393, 490, 607, 748, 889, 1034, 1215, 1404, 1593, 1818, 2031, 2300, 2569, 2810, 3071, 3436, 3753, 4042, 4399, 4796, 5129, 5610, 5967, 6412, 6857, 7242, 7759, 8380, 8809, 9242, 9775, 10460

Offset

0,3

Comments

See A210000 for a guide to related sequences.

Links

Table of n, a(n) for n=0..40.

Mathematica

a = 1; 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, -m, m}]
Table[c1[n, 1], {n, 0, z1}]    (* A209994 *)

Crossrefs

Cf. A210000.

Sequence in context: A187633 A063154 A100500 * A211013 A085473 A051943

Adjacent sequences: A209991 A209992 A209993 * A209995 A209996 A209997

Keyword

nonn

Author

Clark Kimberling, Mar 18 2012

Status

approved