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Summation for a Python function

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    For formatting sake Ive copied a picture of the problem and attached it here: http://i.imgur.com/kOjTy.png

    Im not worried about the coding part right now I feel I can handle that, my main issue is trying to understand how the values in the summation are derived. It seems simple enough, but I cant seem to grasp how they got the 10 values in the example there. Once I understand the summation, the coding should be easy. I just need a bit of guidance in how it all's working.

    2. Relevant equations

    Cn+1 = Ʃ Ck Cn-k from k = 0 to n

    3. The attempt at a solution
    Obviously
    C0 = 1

    Beyond that, here's what my understanding of it seems to be:
    For C1
    k starts at 0
    C1 = C0 * C1-0 + C1 * C1-1

    but this is where I get confused.
     

    Attached Files:

  2. jcsd
  3. Apr 14, 2012 #2

    jambaugh

    User Avatar
    Science Advisor
    Gold Member

    I suspect one defines the process recursively. How many ways can you draw a line segment between vertices? Each way divides the polygon into two smaller polygons.

    You may then have to be careful iterating cases in a way that avoids double counting.
     
  4. Apr 14, 2012 #3
    hmm, i think you are reading the summation notation wrong, Cn+1 doesn't come into the equation, only Cn, the previous term.
    C1 = C0*C0 = 1
    C2 = C0*C1 + C1*C0 = 2
    C3 = C0*C2 + C1*C1 + C2*C0 = 5
    C4 = C0*C3 + C1*C2 + C2*C1 + C3*C0 = 14
    and so on...
     
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