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A210372
Number of 2 X 2 matrices with all elements in {0,1,...,n} and positive even determinant.
4
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 20 2012
EXTENSIONS
Offset corrected by Chai Wah Wu, Nov 27 2016
STATUS
approved