Experience Variable

HI,

I need to operationalise a variable counting the number of times a firm terminated a drug development project. But this count needs to be discounted by a constant (x). The formula that I need to follow is ExpFailure(t)= x*ExpFailure(t-1)+ Failure(t-1). I have operationalised Failure(t-1) (the number of failures that occurred between time t and t-1) but my problem is how to code ExpFailure(t-1) (the value of ExpFailure at time t-1) as its value depends on the value of ExpFailure at t-1? In other words, this formula would take the below values as time goes by:

ExpFailure(1)=x*ExpFailure(0) + Failure (0) = Failure (0) in the first observation ExpFailure(0) is equal to zero as there in no counts of failure events at the start of the observation.
ExpFailure(2)=x*ExpFailure(1) + Failure (1)
ExpFailure(3)=x*ExpFailure(2) + Failure (2)
and so on

My problem is, how do you define a variable which value depends on a previous value of the same variable?

Thanks