The Hilbert function of general unions of lines and double lines in the projective space

We study the Hilbert function of a general union $Xsubset mathbb{P}^3$ of $x$ double lines and $y$ lines. In many cases (e.g. always for $x=2$ and $yge 3$ or for $x=3$ and $yge 2$ or for $xge 4$ and $yge lceil(binom{3x+4}{3} -27x-12)/(3x+2)rceil +3-x$) we prove that $X$ has maximal rank. We give a few examples of $x$ and $y$ for which $X$ has not maximal rank.