1. The problem statement, all variables and given/known data I am a dumb programmer trying to figure out the relationship for a sequence of output. I can't seem to figure it out by guessing, so I assume there's a way to mathematically work this out. Anyways I wrote a program to do discrete event simulation and I have the following numbers on a given input x that represents the % of time the system spends in this state. The numbers are not exactly what they should be because it's simulated, but there's a huge sample so it should be very close. x = 1, f(x) = 0 x = 2, f(x) = 0.063 x = 3, f(x) = 0.156 x = 4, f(x) = 0.26 x = 5, f(x) = 0.366 x = 6, f(x) = 0.467 2. Relevant equations This may have something to do with the fraction 1/4. My system has events that spend 25% of the time doing one thing, then 75% of the time doing another. 3. The attempt at a solution I tried guessing and checking, the only way I know how. I figured 0.25^0 = 1, 0.25^1 = 0.25, 0.25^2 = 0.063, then 0.25^3 = 0.015625 which is close, but one decimal off and finally 0.25^4 = 0.00390625 which isn't even close anymore to the above. I also tried dividing each subsequent output with the last output to try and get some sort of pattern and it seems sporadic. I'm so confused >< Please point me in the right direction!