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A211067
Number of 2 X 2 matrices having all terms in {1,...,n} and positive even determinant.
4
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 31 2012
STATUS
approved