Hyperfine coupling for a spin-one nucleus

For electron spin $s=1/2$, first add orbital and spin angular momenta to obtain $j=L\pm 1/2$. For nuclear spin $I=1$, add again to obtain $F=|j-1|,|j-1|+1,\dots ,j+1$. The projection has $2F+1$ possible values. A hydrogenic bound state still requires $L\le n-1$.