555 timer duty cycle
Try using this website and adjusting the numbers in the following 2 scenarios: -



For the left hand scenario I've entered 10k for R1 and 10k for R2 and got an output high time of 0.1386 seconds. Note the output low time of 0.0693 seconds i.e. 66.6% duty

For the right hand scenario I've frigged the results by making R1 = 19k and R2 = 1k (this is my guesstimate of what R2 will be when parallel with a diode. Note the high-time remains at 0.1386 seconds but the low time is 0.00693 seconds.

Does this help you a little bit in simulating the effect of a diode across R2? Yeah I know it's a bodge but unless you invest in free software from Linear technology called LTSpice I know of no other way without a formula. Here's the link to LTSpice