A211067 Number of 2 X 2 matrices having all terms in {1,...,n} and positive even determinant.

0, 2, 13, 64, 144, 362, 617, 1200, 1776, 2986, 4101, 6264, 8160, 11714, 14657, 20064, 24464, 32266, 38485, 49320, 57752, 72354, 83585, 102632, 117120, 141578, 159917, 190592, 213496, 251370, 279465, 325704, 359640, 415354, 455973

Offset: 1

Author

Clark Kimberling, Mar 31 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A210000.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A210000.

Programs

Mathematica

a = 1; b = n; z1 = 35;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
u[n_] := u[n] = Sum[c[n, 2 k], {k, 0, n^2}]
v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, n^2}]
w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, n^2}]
Table[u[n], {n, 1, z1}]  (* A211066 *)
Table[v[n], {n, 1, z1}]  (* A211067 *)
Table[w[n], {n, 1, z1}]  (* A211068 *)

Formula

a(n) = (A211064(n) - A134506(n))/2. - Chai Wah Wu, Nov 28 2016