A211066 Number of 2 X 2 matrices having all terms in {1,...,n} and nonnegative even determinant.

1, 8, 28, 96, 193, 448, 728, 1360, 1985, 3264, 4420, 6696, 8641, 12296, 15360, 20896, 25361, 33344, 39636, 50680, 59289, 74056, 85376, 104728, 119377, 144032, 162588, 193568, 216585, 254880, 283096, 329656, 363881, 419856, 460804

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: A331454 A333278 A333283 * A095857 A184606 A054114

Adjacent sequences: A211063 A211064 A211065 * A211067 A211068 A211069

Keyword

nonn

Author

Clark Kimberling, Mar 31 2012

Status

approved