does a yeast starter from washed yeast count as a generation?

I have read that washing yeast works well for up to 5 generations but know I am wondering if does a yeast starter from washed yeast count as a generation? What if you ended up stepping up the size of a starter, will this count for a generation? (ie, if there a certain period of time for yeast activity to count as a generation?)

My gut says that making the starter will not count as a generation but since we had bad mexican food for dinner last night I am not wanting to trust my gut instincts.

I would say no