TITLE: When do colonizers start marrying cousins?
QUESTION [5 upvotes]: Suppose a group of humans, with $n$ males and $n$ females, colonizes another planet.  Suppose they all pair up in the usual way, and each couple has two children--one boy and one girl.  Then the process repeats. 
Question: How many generations can pass before somebody has to marry their cousin?

EDIT: 
To clarify:

Each member of a generation marries someone of the same generation.  
We assume that the original colonists are all unrelated. 
Nobody marries their sibling, though if you broaden the definition of "cousin" to include "anybody who shares a common ancestor" then you don't need to make this assumption.  (So in light of the above point, the question can be restated "How many generations can pass before someone marries a relative.")

REPLY [3 votes]: If no-one marries a relative for the first $k$ generations, then everyone in the next generation will have $2^k$ ancestors from the first generation, which must all be distinct. So we must have $2^k\leq 2n$.
If $2n$ is a power of $2$, say $2n=2^k$ then you can have $k$ iterations without anyone marrying a relative. You start of with $2^k$ family groups of $2^0$ people each; pair off groups and have everyone marry someone from the paired group, resulting in $2^{k-1}$ groups of $2^1$ people each in the next generation. Carry on in this manner, so that after $j$ generations you have $2^{k-j}$ family groups of $2^j$ people each, with different groups being unrelated. (After the first generation, every group has the same number of each sex, so the pairing off can be done ok.)
If $2n$ is not a power of $2$ you will have to work a bit harder to get a construction for $\lfloor\log_2(2n)\rfloor$ generations, but I imagine it's possible.