I think you're looking for a stroboscopic mode, where the flash fires multiple times in one exposure.

The Nikon SB-800 and SB-900 have this feature — Nikon calls it "repeating mode". (The SB-700 does not.) That probably doesn't fit your definition of "cheap", though.

Another option is the Sigma EF610 DG Super, which you can get for $225, or the Nissin Di866 for around $300. These third-party flashes are reverse-engineered "dedicated flashes", which come in specific versions for Nikon, Canon, Pentax, etc., and have advanced features rivaling the system-branded models.

Metz has a stroboscopic mode too, but only on their $350+ model. Also, the cheaper Sigma EF610DG ST (presumably for "standard", as opposed to "super") and the lower-end Nissin models don't have the feature.

The Promaster 7500EDF is another $250 option, but I hesitate to recommend it, because a) it has a more-limited version of the feature with a max of 10 flashes in a sequence and b) for Pentax at least Promaster has done a poor job keeping up compatibility with new camera bodies, and while they might be better with Nikon I wouldn't count on it.