[math-fun] nonrecursive doubling of continued fractions

I have been reading Bill Gosper's and Adolph Hurwitz' recursive presentation of finding the half or double(and more) of a continued fraction. I have been working on unrolling the recursion in the case of multiplying and dividing a continued fraction by 2 and 3. Does anyone know(or care) about such a nonrecursive (and general)expression or algorithm? I find that this unrolling for a general continued fraction has some very interesting properties. Art DuPre'