Excluding Social Dancing where you would be taught 1a2a3 and so on. Counting that way will produce a count of 1/2 1/2 1/2.
Are you not aware that an "a" count has a value of 1/4?
Counting "1,,a2" gives you a value of 3/4, 1/4, whole. Counting "1 AND 2" gives you a value of 1/2, 1/2, whole. There's a big difference.
"a" = 1/4 beat, borrowed from the previous count.
"and" = 1/2 beat, borrowed from the previous count.
There are two exceptions to this rule:
(1) When the music has a "swing feel", each beat is divided into
thirds, not halves or quarters. Therefore, in swing music "a" has a value of 1/3 beat. (The "and" count would theoretically be 2/3, but an "and" without an "a" is extremely uncommon, and basically non-existent as a dance rhythm to swing music).
(2) When an "a" piggybacks and "and", the "a" steals the time from the "and", which has in turn stolen time from the original beat. So in straight-time music, "1--and-a-2" amounts to 1/2, 1/4, 1/4, whole, meaning the "and" and the "a" both have an equal value of 1/4. In swing feel, they both have an equal value of 1/3.
Regards,
Jonathan