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A210371 Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative even determinant.

%I A210371 #10 Nov 28 2016 03:58:30
%S A210371 1,10,48,112,285,490,968,1448,2465,3410,5280,6904,10021,12610,17400,
%T A210371 21312,28321,33866,43704,51336,64661,74898,92416,105680,128297,145234,
%U A210371 173712,194928,230333,256410,299776
%N A210371 Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative even determinant.
%C A210371 See A210000 for a guide to related sequences.
%H A210371 Chai Wah Wu, <a href="/A210371/b210371.txt">Table of n, a(n) for n = 0..10000</a>
%F A210371 a(n) = (A210369(n) + A059306(n))/2. - _Chai Wah Wu_, Nov 27 2016
%t A210371 a = 0; b = n; z1 = 30;
%t A210371 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A210371 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A210371 u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, n^2}]
%t A210371 v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, n^2}]
%t A210371 w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, n^2}]
%t A210371 Table[u[n], {n, 0, z1}] (* A210371 *)
%t A210371 Table[v[n], {n, 0, z1}] (* A210372 *)
%t A210371 Table[w[n], {n, 0, z1}] (* A210373 *)
%Y A210371 Cf. A210000.
%K A210371 nonn
%O A210371 0,2
%A A210371 _Clark Kimberling_, Mar 20 2012