A210372 Number of 2 X 2 matrices with all elements in {0,1,...,n} and positive even determinant.

0, 0, 17, 48, 172, 320, 713, 1112, 2016, 2840, 4561, 6056, 8964, 11400, 15977, 19648, 26400, 31744, 41257, 48664, 61620, 71512, 88689, 101680, 123800, 140376, 168449, 189232, 224108, 249840, 292545

Offset: 0

Author

Clark Kimberling, Mar 20 2012

Keywords

• nonn

Comments

See A210000 for a guide to related sequences.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A210000.

Programs

Mathematica

a = 0; b = n; z1 = 30;
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, 0, z1}] (* A210371 *)
Table[v[n], {n, 0, z1}] (* A210372 *)
Table[w[n], {n, 0, z1}] (* A210373 *)

Formula

a(n) = (A210369(n) - A059306(n))/2. - Chai Wah Wu, Nov 27 2016

Extensions

Offset corrected by Chai Wah Wu, Nov 27 2016