NI's counters don't (quite) work that way.
The simple standard operation is that there are registers to hold integer values for both "Low Ticks" and "High Ticks" where the term "Ticks" refers to the active edge of the signal.
Both Low and High Ticks must be >= 2. 2 Ticks High and 2 Ticks low means 4 Ticks per full cycle, so you can only generate square waves on Ctr1 and Ctr2 that divide down the 50 kHz from Ctr0 by even integers >= 4. Odd integers divide into different Low and High Tick #'s, making the output non-square.
If you get to control Ctr0 yourself, then you can just define Ctr1 and Ctr2 with the desired frequencies (which just get converted to Tick counts behind the scenes), set them up to Start Trigger from the non-active edge of Ctr0, and start Ctr1 & Ctr2 *before* starting Ctr0.
But I assume this is a trial run to check things out with your own Ctr0 signal whereas your real app will need to react to an external clock that it doesn't control. So let's get to some other counter tricks.
1. The default mode for counter output is "toggle" mode. Count down Low Ticks to 0, toggle the output state, Count down High Ticks to 0, toggle the output state, etc. You can change that to "pulse" mode so that each countdown to 0 results in a very brief high-low pulse. The duration is (I think) one cycle of the device's timebase which will likely be 100 MHz on modern-era DAQ devices I know of. So you definitely won't get square output, but using this mode *does* let you divide down an external frequency by 2 or 3, as well as all the other integers >=4 that are also supported by the default "toggle" mode.
2. (This is the approach I'd prefer.) You can set up Ctr1 and Ctr2 to output retriggerable single pulses. You get single pulses by never calling DAQmx Timing (see the shipping examples as a guide). You need a DAQmx Trigger property node to set the "retriggerable?" property to True.
Assuming we react to rising edges from Ctr0, I'd likely define the absolute minimum value of 2 for both Low Ticks and Initial Delay. I'd set High Ticks to try to match the pulse width of the Ctr0 signal. If that's something you can't know ahead of time, I'd probably do a little pre-run sneak peak by briefly running a counter input task that measures it.
-Kevin P
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