All this talk about high current LEDs ... time for me to add another twist. Many of us use the WS2801 for driving RGB LEDs that don't require more then 20mA per channel. It works great as each channel on the WS2801 can provide up to 50mA in constant current, or up to 100mA in constant voltage, though I haven't seen anyone do that yet.
One of the lesser known configurations is the ability to drive high current LEDs with an external switch, like this:

The part I'm having trouble with is understanding the various formulas that go with that. This is what the datasheet says:

For one, what is ß (Beta)?
If I'm putting 3 LEDs in series, each with a voltage drop of 3.4, forward current of 140mA, and a 12V supply (as opposed to the 24V in that figure), I calculate a current limiting resistor value of 12.86 Ohm, or a more standard value of 15 Ohm.
How do I work that in here? How do I figure out what the current on the base and collector is? The value of XOUT is calculated using the value of RXFB - the 'X' refers to a particular channel, be it R, G, or B, so you can think of the values as 'GOUT' and 'RGFB' for the Green channel. Voltage on XOUT is -0.3V to 7V (or whatever VCC is, really.)
I just don't know how to calculate the different values that I need for the resistor and specific NPN that I would need to match the LEDs details.
Anyone feel like shedding some light please?