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A210371
Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative even determinant.
4
1, 10, 48, 112, 285, 490, 968, 1448, 2465, 3410, 5280, 6904, 10021, 12610, 17400, 21312, 28321, 33866, 43704, 51336, 64661, 74898, 92416, 105680, 128297, 145234, 173712, 194928, 230333, 256410, 299776
OFFSET
0,2
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: A304626 A121075 A121073 * A195023 A353620 A277229
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved