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A211066 Number of 2 X 2 matrices having all terms in {1,...,n} and nonnegative even determinant.

%I A211066 #7 Nov 29 2016 03:01:12
%S A211066 1,8,28,96,193,448,728,1360,1985,3264,4420,6696,8641,12296,15360,
%T A211066 20896,25361,33344,39636,50680,59289,74056,85376,104728,119377,144032,
%U A211066 162588,193568,216585,254880,283096,329656,363881,419856,460804
%N A211066 Number of 2 X 2 matrices having all terms in {1,...,n} and nonnegative even determinant.
%C A211066 For a guide to related sequences, see A210000.
%H A211066 Chai Wah Wu, <a href="/A211066/b211066.txt">Table of n, a(n) for n = 1..10000</a>
%F A211066 a(n) = (A211064(n) + A134506(n))/2. - _Chai Wah Wu_, Nov 28 2016
%t A211066 a = 1; b = n; z1 = 35;
%t A211066 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211066 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211066 u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, n^2}]
%t A211066 v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, n^2}]
%t A211066 w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, n^2}]
%t A211066 Table[u[n], {n, 1, z1}]  (* A211066 *)
%t A211066 Table[v[n], {n, 1, z1}]  (* A211067 *)
%t A211066 Table[w[n], {n, 1, z1}]  (* A211068 *)
%Y A211066 Cf. A210000.
%K A211066 nonn
%O A211066 1,2
%A A211066 _Clark Kimberling_, Mar 31 2012