/sci/ - Science & Math

In pic related there is an exercise which asks to prove that f(m,n) = 2^m(2n+1) - 1 is bijective (for the purpose of showing that N^2 is equinumerous to N). I have proven that it's injective, but am struggling to show that it's onto. My approach was to break it into even and odd cases. When even, finding the ordered pair that maps is straight forward but I can't figure out how to map odd numbers. any advice?