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Homework Help: Discrete Math: Self-referential formula

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Figure out a self-referential formula for the number of handshakes required for a group of n aliens to introduce themselves by hand-calculating a few small values and coming up with a solution.

    2. Relevant equations

    We are given:

    Let H(n) be the number of handshakes for a group of n aliens to introduce themselves. Then H(n) = [n(n-1)(n-2)]/6

    3. The attempt at a solution

    I couldn't find anything in my textbook about how to derive a self-referential formula. I tried hand-calculating a few small values for H(n) by substituting n for 1, 2, 3, 4, 5 and 6.

    H(1) = 0
    H(2) = 0
    H(3) = 1
    H(4) = 4
    H(5) = 10
    H(6) = 20

    I'm not sure what to do next. How do I derive a self-referential formula from this information?
  2. jcsd
  3. Nov 20, 2011 #2


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    Science Advisor
    Homework Helper

    First off, I'm not sure what this introducing yourself is supposed to mean. If you have 2 aliens and they want to introduce themselves, shouldn't they shake hands? Then they are introduced. That would mean H(2)=1. Your formula would seem to suggest they have to introduce in groups of three. Might be why they are 'alien'. Can you state the whole problem?
  4. Nov 21, 2011 #3
    To find a self referential formula, try to express H(n) as a function of H(n-1)
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