Analogue-sequencer

I've been reading the last few posts about entering 8th and 16th 
notes etc. and one thing i'm curious about that is, it's obvious how 
to change the note values and duration but what i'd like to know is 
can the sequencer trigger notes on the "and" counts?... ie; where the 
quarter note is counted 1, 2, 3 "and" 4 "and" .... and so forth. Or 
am i so bogged down in traditional theory and thinking that i don't 
see the function or see the equivalent on the machine?
Kind regards
john duval