title: n steps with 1, 2 or 3 steps taken. How many ways to get to the top?
body: <p>If we have n steps and we can go up 1 or 2 steps at a time, there is a Fibonacci relation between the number of steps and the ways to climb them. IF and ONLY if we do not count 2+1 and 1+2 as different.</p>
  
  <p>However, this no longer the case, as well as having to add we add a third option, taking 3 steps. How do I do this?</p>
  
  <p>What I have:</p>
  
  <pre><code>1 step = 1 way
  2 steps = 2 ways: 1+1, 2
  3 steps = 4 ways: 1+1+1, 2+1, 1+2, 3
  </code></pre>
  
  <p>I have no idea where to go from here to find out the number of ways for n stairs</p>
  
  <p>I get 7 for n = 4 and 14 for n= 5 i get 14+7+4+2+1 by doing the sum of all the combinations before it. so ways for n steps = n-1 ways + n-2 ways + .... 1 ways  assuming i kept all the values.  DYNAMIC programming.
  1 2 and 3 steps would be the base-case is that correct?</p>