How to increase video speed and frame rate without duplicating frames

As happens regularly to me, after spending hours trying to figure it out before asking for help, I find the solution myself just minutes after asking.

It turns out avconv isn't the better replacement to ffmpeg that I thought it was when Linux Mint, IIRC, removed ffmpeg from the official repository in favor of avconv. Anyway, ffmpeg is back and I installed it and found the equivalent command that doesn't duplicate frames:

ffmpeg -i input_30fps.avi -vcodec h264 -an -vf "fps=60, setpts=(1/200)*PTS" output_200x_60fps.avi