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A211064 Number of 2 X 2 matrices having all terms in {1,...,n} and even determinant.

%I A211064 #12 May 12 2025 10:13:00
%S A211064 1,10,41,160,337,810,1345,2560,3761,6250,8521,12960,16801,24010,30017,
%T A211064 40960,49825,65610,78121,100000,117041,146410,168961,207360,236497,
%U A211064 285610,322505,384160,430081,506250,562561,655360,723521,835210
%N A211064 Number of 2 X 2 matrices having all terms in {1,...,n} and even determinant.
%C A211064 For a guide to related sequences, see A210000.
%H A211064 Chai Wah Wu, <a href="/A211064/b211064.txt">Table of n, a(n) for n = 1..10000</a>
%F A211064 a(n) + A211065(n) = n^4.
%F A211064 From _Chai Wah Wu_, Nov 27 2016: (Start)
%F A211064 a(n) = n^4 - (2*n + 1 -(-1)^n)^2*(6*n + 1 -(-1)^n)*(2*n - 1 + (-1)^n)/128.
%F A211064 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n > 9.
%F A211064 G.f.: x*(-x^7 - 9*x^6 - 51*x^5 - 59*x^4 - 83*x^3 - 27*x^2 - 9*x - 1)/((x - 1)^5*(x + 1)^4). (End)
%t A211064 a = 1; b = n; z1 = 35;
%t A211064 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211064 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211064 u[n_] := Sum[c[n, 2 k], {k, -2*n^2, 2*n^2}]
%t A211064 v[n_] := Sum[c[n, 2 k - 1], {k, -2*n^2, 2*n^2}]
%t A211064 Table[u[n], {n, 1, z1}] (* A211064 *)
%t A211064 Table[v[n], {n, 1, z1}] (* A211065 *)
%Y A211064 Cf. A210000.
%K A211064 nonn
%O A211064 1,2
%A A211064 _Clark Kimberling_, Mar 31 2012