I am prototyping a staircase lighting circuit using an Arduino and a TLC5940 led driver. The led supply voltage will be 12v. The leds draw 20ma ea at 3.4v. There will be 2 leds per step/channel. Any opinions as to whether it would be better to wire the leds for each step/channel in series or parallel? I'm kinda leaning toward series so that if an led would short the current to the second would still be whatever the maximum current was set to (20ma). Whereas in parallel the maximum current would have to be set to double the typical led current of 20ma to have both leds illuminate brightly. In that case if an led should short the other led would have 40ma going through it. - Scotty
Remember that the TLC5940's output channels effectively act like a current limiting resistor. So whatever voltage your LEDs do not drop, the output channel does. So look at power dissipation of the TLC5940 per channel.
Parallel:
LEDs drop 3.4V, leaving 12-3.4 = 8.6V on the TLC5940 Output Channel. You're drawing 40mA (assuming you set IRef to 40mA in the parallel case), so that's 344mW per channel.
Series:
LEDs drop 6.8V, leaving 12-6.8 = 5.2V on the TLC5940 Output Channel. You're drawing 20mA (assuming you set IRef to 20mA in the series case), so that's 104mW per channel.
Even if you increased the Series-case to 40mA per channel, your power dissipated by the TLC5940 would still only be 208mW per channel. Of course, if that's more than the LEDs can handle, you won't have to worry for very long... 
You could make the parallel-case more efficient by not using so a large difference in LED supply and LED forward voltage.
Thanks for responding because since you revealed that the TLC5940 will be burning up the voltage not used by the leds, It makes sense for me to design the circuit to run entirely off of 5V and wire the leds in parallel. This simplifies things a bit and will also save a few bucks since I was going to buy a small 12VDC power supply and regulate it down for the ICs. - Scotty