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

0,3

Comments

See A210000 for a guide to related sequences.

Links

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

Formula

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

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 *)

Crossrefs

Cf. A210000.

Sequence in context: A051869 A297818 A297988 * A239130 A181426 A029487

Adjacent sequences: A210369 A210370 A210371 * A210373 A210374 A210375

Keyword

nonn

Author

Clark Kimberling, Mar 20 2012

Extensions

Offset corrected by Chai Wah Wu, Nov 27 2016

Status

approved