title: Functional recurrence on a constant?
body: <p>I am given this recurrence relation:</p>
  
  <pre><code>T (n) = T (n − a) + T (a) + cn
  </code></pre>
  
  <p>C > 0 , a >= 1 ..</p>
  
  <p>my problem is with T (a) , I don't understand how you can "recurs" a constant??</p>
  
  <p>Like, if am trying to build a recurrence tree, I would go by doing this:</p>
  
  <pre><code>T (n) =&gt;  cn            =&gt;         cn
           /  \                    /    \
        T(a)  T(n - a)           ca      c*(n-a)
                               /    \     /     \
                              ??    ??  T(n-2a)  T(a)
  </code></pre>
  
  <p>You see what I mean? What does T(a) represent??</p>
  
  <p>Any resource will be much appreciated. Thanks.</p>
  
  <p>OR, think of it iteratively:</p>
  
  <pre><code>T (n) = T (n − a) + T (a) + cn
  T (n) = T (n -2a) + T (a) + ????
  </code></pre>