A210371 - OEIS

%I #10 Nov 28 2016 03:58:30

%S 1,10,48,112,285,490,968,1448,2465,3410,5280,6904,10021,12610,17400,

%T 21312,28321,33866,43704,51336,64661,74898,92416,105680,128297,145234,

%U 173712,194928,230333,256410,299776

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

%C See A210000 for a guide to related sequences.

%H Chai Wah Wu, <a href="/A210371/b210371.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (A210369(n) + A059306(n))/2. - _Chai Wah Wu_, Nov 27 2016

%t a = 0; b = n; z1 = 30;

%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, n^2}]

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

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

%t Table[u[n], {n, 0, z1}] (* A210371 *)

%t Table[v[n], {n, 0, z1}] (* A210372 *)

%t Table[w[n], {n, 0, z1}] (* A210373 *)

%Y Cf. A210000.

%K nonn

%O 0,2

%A _Clark Kimberling_, Mar 20 2012