# Discrete Math: Self-referential formula

• SolarMidnite

## Homework Statement

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.

## Homework 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

## 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?

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?

To find a self referential formula, try to express H(n) as a function of H(n-1)