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A210372 Number of 2 X 2 matrices with all elements in {0,1,...,n} and positive even determinant.

%I A210372 #11 Nov 28 2016 03:58:22
%S A210372 0,0,17,48,172,320,713,1112,2016,2840,4561,6056,8964,11400,15977,
%T A210372 19648,26400,31744,41257,48664,61620,71512,88689,101680,123800,140376,
%U A210372 168449,189232,224108,249840,292545
%N A210372 Number of 2 X 2 matrices with all elements in {0,1,...,n} and positive even determinant.
%C A210372 See A210000 for a guide to related sequences.
%H A210372 Chai Wah Wu, <a href="/A210372/b210372.txt">Table of n, a(n) for n = 0..10000</a>
%F A210372 a(n) = (A210369(n) - A059306(n))/2. - _Chai Wah Wu_, Nov 27 2016
%t A210372 a = 0; b = n; z1 = 30;
%t A210372 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A210372 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A210372 u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, n^2}]
%t A210372 v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, n^2}]
%t A210372 w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, n^2}]
%t A210372 Table[u[n], {n, 0, z1}] (* A210371 *)
%t A210372 Table[v[n], {n, 0, z1}] (* A210372 *)
%t A210372 Table[w[n], {n, 0, z1}] (* A210373 *)
%Y A210372 Cf. A210000.
%K A210372 nonn
%O A210372 0,3
%A A210372 _Clark Kimberling_, Mar 20 2012
%E A210372 Offset corrected by _Chai Wah Wu_, Nov 27 2016