Enter this line in a Mathematica cell:

f[mu_,x_]=mu*x*(1-x)


In a separate cell enter all of the following (modify mu, tail, and maxiterates as needed):

mu=3.55;
maxiterates=300;
tail=20;
x=.5;
For[i=1,i<maxiterates,i++,
x=f[mu,x];
If[i>maxiterates-tail,Print[x]]
]