A211067 - OEIS

%I #7 Nov 29 2016 03:01:20

%S 0,2,13,64,144,362,617,1200,1776,2986,4101,6264,8160,11714,14657,

%T 20064,24464,32266,38485,49320,57752,72354,83585,102632,117120,141578,

%U 159917,190592,213496,251370,279465,325704,359640,415354,455973

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

%C For a guide to related sequences, see A210000.

%H Chai Wah Wu, <a href="/A211067/b211067.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A211064(n) - A134506(n))/2. - _Chai Wah Wu_, Nov 28 2016

%t a = 1; b = n; z1 = 35;

%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, 1, z1}]  (* A211066 *)

%t Table[v[n], {n, 1, z1}]  (* A211067 *)

%t Table[w[n], {n, 1, z1}]  (* A211068 *)

%Y Cf. A210000.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 31 2012