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.
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?