A211149 Number of 2 X 2 nonsingular matrices having all terms in {-n,...,0,...,n}.

48, 496, 2112, 6016, 13808, 27248, 48896, 81152, 127280, 190576, 275264, 384768, 524784, 699376, 914176, 1175040, 1488688, 1860208, 2298304, 2808320, 3399280, 4079088, 4856704, 5738624, 6736944, 7859824, 9117376, 10519424

Offset: 1

Author

Clark Kimberling, Apr 04 2012

Keywords

• nonn

Comments

A211149(n) + A209981(n) = (2n+1)^4 for n>0.

It appears that 16 divides A211149(n).

For a guide to related sequences, see A210000.

Crossrefs

Cf. A210000.

Programs

Mathematica

a = -n; b = n; z1 = 30;
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]
Table[c[n, 0], {n, 1, z1}]   (* A209981 *)
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 1, m}]
t = Table[c1[n, 2*n^2], {n, 1, z1}]   (* A211148 *)
2 t   (* A211149 *)
t/8   (* integers *)