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A211157 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and positive even determinant. 4

%I

%S 4,164,528,1968,3844,8836,14144,26176,37540,61188,82192,123120,157924,

%T 223268,276608,374272,452420,591524,700752,891760,1038980,1293700,

%U 1487744,1818112,2067172

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

%C For a guide to related sequences, see A210000.

%t a = -n; b = n; z1 = 25;

%t t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]

%t c[n_, k_] := c[n, k] = Count[t[n], k]

%t u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, 2*n^2}]

%t v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, 2*n^2}]

%t w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, 2*n^2}]

%t u1 = Table[u[n], {n, 1, z1}] (* A211156 *)

%t v1 = Table[v[n], {n, 1, z1}] (* A211157 *)

%t w1 = Table[w[n], {n, 1, z1}] (* A211158 *)

%t (u1 - 1)/4 (* integers *)

%t v1/4 (* integers *)

%t w1/4 (* integers *)

%Y Cf. A210000.

%K nonn

%O 1,1

%A _Clark Kimberling_, Apr 05 2012

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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)