@Dennis Lomas

Yes, if you have one row, you can get either the row prior or the next row fairly easily.

Each row, \\(i\\), has \\(2^i\\) elements (with \\(i\\) starting at 0). Using a new function \\(h(i,j) = g(2^i+j)\\) where \\(g\\) is defined by Patrick above (#3), and \\(j \in [0,2^i-1]\\) is used to index into the row itself.

We can get see that \\(h(i,j) = h(i,2j)\cdot h(i,2j+1)\\). This is the same tree structure mentioned by Michael Hong in #15 (see the wikipedia page on the Calkin-Wilf tree for a good visualization of this).

To get the *next* row, we know that \\(h(i,j) = \frac{a}{b}\\) for some \\(a,b\\). \\(h(i,2j) = \frac{a}{a+b}\\) and \\(h(i,2j+1) = \frac{a+b}{b}\\).