Can every recursion be converted into iteration?

Question

A reddit thread brought up an apparently interesting question:

Tail recursive functions can trivially be converted into iterative functions. Other one

Answer 1

Here is an iterative algorithm:

def howmany(x,y)
  a = {}
  for n in (0..x+y)
    for m in (0..n)
      a[[m,n-m]] = if m==0 or n-m==0 then 1 else a[[m-1,n-m]] + a[[m,n-m-1]] end
    end
  end
  return a[[x,y]]
end