It seems that both AI fail to compute the correct radius of the osculating circle at the two points, i.e. the value of "r" that enters the acceleration v2/r. It should be r = 2R and R/4 instead of R. If you enter these two, I have the impression you should find 8 again :-)
That's in fact a good way to avoid having to derive my eq. (1) and use something else instead.