It's a matter of periods in the sequence of numbers generated by the PRNG. If the output of the PRNG has a single period that is of length $2^n$, then you can avoid repetition by appropriately recording the section that you have already used. Thus if you start from $0$ and get the first time to $g_1$, the next time you start from $g_1$ and get to $g_2$, etc. until you have used up the entire period (keep a count of the numbers generated in order to detect that). PRNGs that generate numbers in $[0, 2^{n-1}]$ may not necessarily have the maximal period length of $2^n$. One special kind of PRNGs that have the maximal period length are based on the so-called permutation polynomials mod $2^n$. I used it in one of my software ([s13.zetaboards.com/Crypto/topic/7355166/1/][1]), where a literature reference to permutation polynomials as well as a practical  implementation of PRNGs based on them are given.


  [1]: http://s13.zetaboards.com/Crypto/topic/7355166/1/