Question: A group of 10 people begin a chain letter, with each person sending the letter to four other people. Each of these people sends the letter to four additional people.
a) Find a recurrence relation for the number of letters sent at the nth stage of this chain letter, if no person ever receives more than one letter.
b) What are the initial conditions for the recurrence relation in part (a)?
c) How many letters are sent at the nth stage of the chain letter?