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

1,2

Comments

For a guide to related sequences, see A210000.

Links

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

Formula

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

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 *)

Crossrefs

Cf. A210000.

Sequence in context: A353177 A089130 A081340 * A296435 A127531 A266633

Adjacent sequences: A211064 A211065 A211066 * A211068 A211069 A211070

Keyword

nonn

Author

Clark Kimberling, Mar 31 2012

Status

approved