Pulldown(clip, int a, int b)
 a:b Pulldown
In general, a:b pulldown (also called telecine) means that the first frame is represented by "a" fields of video, the second frame is represented by "b" fields of video, which is repeated till the end of the clip. inverse telecine: means undoing the telecine.
2:3 or 3:2 pulldown: 23.976 -> 29.97 by adding duplicate fields in the following way: Thus the first frame is represented by two fields of video, the second frame by three fields of video, which is repeated to the end of the clip:
source: AtAb BtBb CtCb DtDb (four frames)
2:3 pulldown: AtAb BtBb BtCb CtDb DtDb (five frames)
3:2 pulldown: AtAb AtBb BtCb CtCb DtDb (five frames)
 Pulldown as AviSynth filter
Pulldown(a,b) (with a < b) selects frames a, b, 5+a, 5+b, 2*5+a, 2*5+b, ... So the filter simply selects two out of every five frames of the source video. The frame rate is reduced to two-fifths of its original value. Note that a a:b telecide can be undone by Pulldown(a,b) if a+b=5.
is the same as undoing a 2:3 (or 3:2) pulldown (ie 29.97 -> 23.976).
Suppose you have material on which 2:3 pulldown is applied, that is
AtAb BtBb CtCb DtDb => AtAb BtBb BtCb CtDb DtDb (five frames)
The reason you need to use DoubleWeave first is that many capture cards sometimes recombine fields in the "wrong" way. In terms of fields, the 3:2 pulldown sequence is simply "At Ab Bt Bb Bt Cb Ct Db Dt Db ...", where "A" through "D" represent the original film frames (before the broadcaster telecined it). But many capture cards the fields into frames with no respect for the pulldown pattern, and you get this:
AtAb BtAb BtBb BtBb BtCb CtCb CtDb DtDb DtDb
Pulldown(0,3) selects frames 0, 3, 5+0, 5+3, 10+0, 10+3, ...
AtAb BtAb BtBb BtBb BtCb CtCb CtDb DtDb DtDb * * * *
AtAb BtBb CtCb DtDb