Why don't we consider the negative values of $k_x, k_y$ and $k_z$ when we compute the density of states of a 3D infinit square well?

I watched some derivations of the density of states in a square box of length L with potential $V=0$ for the points inside the box and $V=infty$ outside the box.
Using separation of variable one can get $frac{2mE}{hbar^2} = k_x^2+k_y^2+k_z^2$ with $k_j = frac{pi}{L}n_j$ and $n_j$ an integer.
Defining $k^2 = k_x^2+k_y^2+k_z^2$ and assuming $k$ is very big we can calculate how many different wave functions there are with a $k$ having a length between $k$ and $k+dx$ by taking the volume of the shell of a sphere with radius $k$, which is $4pi k^2dk$ and divide this by the volume $(frac{pi}{L})^3$. We must multiply the result by $2$ since each combination of $k_j$ can have two different spins.
Summing up I would have said that the density of states is:
$g(k)dk = 2frac{4pi k^2dk}{(frac{pi}{L})^3}$

The thing is the solution says that we only consider the positive $n_j$ so we should multiply the whole thing with $1/8$. I don’t understand why wave function with negative $n_j$ should not be taken into account since for example a wave function with $n_x=1, n_y=2, n_z=3$ does not have the same "direction" as a wave with $n_x=-1, n_y=2, n_z=3$ so I don’t get why we shouldn’t count both.