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A211157 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and positive even determinant.

%I A211157 #6 Jan 10 2017 22:06:47
%S A211157 4,164,528,1968,3844,8836,14144,26176,37540,61188,82192,123120,157924,
%T A211157 223268,276608,374272,452420,591524,700752,891760,1038980,1293700,
%U A211157 1487744,1818112,2067172
%N A211157 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and positive even determinant.
%C A211157 For a guide to related sequences, see A210000.
%t A211157 a = -n; b = n; z1 = 25;
%t A211157 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211157 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211157 u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, 2*n^2}]
%t A211157 v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, 2*n^2}]
%t A211157 w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, 2*n^2}]
%t A211157 u1 = Table[u[n], {n, 1, z1}] (* A211156 *)
%t A211157 v1 = Table[v[n], {n, 1, z1}] (* A211157 *)
%t A211157 w1 = Table[w[n], {n, 1, z1}] (* A211158 *)
%t A211157 (u1 - 1)/4 (* integers *)
%t A211157 v1/4 (* integers *)
%t A211157 w1/4 (* integers *)
%Y A211157 Cf. A210000.
%K A211157 nonn
%O A211157 1,1
%A A211157 _Clark Kimberling_, Apr 05 2012