I was working on the 3D isotropic harmonic oscillator and I found that the energies are given by:
Which has a degeneracy of $\tfrac12(n+1)(n+2)$. However, when dealing with the anisotropic case, I'm not sure if there's a degeneracy in energies. For example, for the 2D anisotropic harmonic oscillator with frequencies $\omega$ and $3\omega$, I found the energies to be:
$$E=\hbar\omega (n_x +3n_y +2)$$
For example here, for $n=1$ we can either have $n_x=1$ so $E_1=3\hbar\omega$ or $n_y=1$ so $E_2=5\hbar\omega$. For $n=2$, we can have $n_x=2$ so $E_2=4\hbar\omega$ or $n_y=2$ so $E_2=8\hbar\omega$ or $n_x=1,n_2=1$ so $E_2=6\hbar\omega$. So there seems to be no degeneracy, but I'm not sure as this is the first time I've found this problem.