How to construct a sequence with a pattern in R

I would like to construct a sequence with length 50 of the following type: Xn+1=4*Xn*(1-Xn). For your information, this is the Logistic Map for r=4. In the case of the Logistic Map with parameter r = 4 and an initial state in (0,1), the attractor is also the interval (0,1) and the probability measure corresponds to the beta distribution with parameters a = 0.5 and b = 0.5. (The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations). How can I do this in R? Thank you very much!