Iirc it costs 1 HaP per tick for the first X ticks (I don't recall the precise value of X, possibly 20) then 1.5 per tick for the next X after that, then 2.25 per tick for the next X after that, etc.
You also gain 1 HaP per tick because you gain 1 AIP per tick (and also lose 2 AIP per tick, giving a net of -1 but a positive effect on the floor).
The first X ticks still cost HaP in the sense that if you'd gained that AIP in some other way you'd be gaining HaP, not just holding steady on it.