title: Find the formula of this binary recurrence equation? f(m,n) = f(m-1,n) + f(m,n-1)
body: <p><strong>SORRY GUYS! MY MISTAKE! Thanks for your reminder, I found out f(0,k) == f(k,0) == 1. This question is about how to count the number of shortest paths from grid (0,0) to (m,n).</strong></p>
  
  <p>I have to solve the following equation now, find out exactly what f(m,n) equal to.</p>
  
  <pre><code>1) f(m,n) = 0 : when (m,n) = (0,0)
  **2) f(m,n) = 1 : when f(0,k) or f(k,0)**
  3) f(m,n) = f(m-1,n) + f(m,n-1) : when else
  </code></pre>
  
  <p>for example: </p>
  
  <pre><code>1) f(0,0) = 0; 
  2) f(0,1) = 1; f(2,0) = 1; 
  3) f(2,1) = f(1,1) + f(2,0) = f(0, 1) + f(1, 0) + f(2, 0) = 1 + 1 + 1 = 3  
  </code></pre>
  
  <p>I remember there is a standard way to solve such kinds of binary recurrence equation as I learned in my algorithm class several years ago, but I just cannot remember for now. </p>
  
  <p>Could anyone give any hint? Or a keyword how to find the answer?</p>