A211156 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and even nonnegative determinant.

37, 293, 817, 2513, 4677, 10149, 15873, 28545, 40581, 65093, 86769, 128977, 164581, 231173, 285953, 385153, 464357, 605477, 715889, 909201, 1058501, 1315237, 1510721, 1844289, 2095429

Offset

1,1

Comments

For a guide to related sequences, see A210000.

Links

Table of n, a(n) for n=1..25.

Mathematica

a = -n; b = n; z1 = 25;
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]
u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, 2*n^2}]
v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, 2*n^2}]
w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, 2*n^2}]
u1 = Table[u[n], {n, 1, z1}] (* A211156 *)
v1 = Table[v[n], {n, 1, z1}] (* A211157 *)
w1 = Table[w[n], {n, 1, z1}] (* A211158 *)
(u1 - 1)/4 (* integers *)
v1/4 (* integers *)
w1/4 (* integers *)

Crossrefs

Cf. A210000.

Sequence in context: A086840 A190418 A200889 * A217642 A197340 A165373

Adjacent sequences: A211153 A211154 A211155 * A211157 A211158 A211159

Keyword

nonn

Author

Clark Kimberling, Apr 05 2012

Status

approved