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Math 184

Homework 3

Question 2. Let Φ(x) be the generating function for partitions of n into two prime numbers, and suppose

Determine the smallest value of n such that an = 3.                                                                                         [4]

Question 3. Let an  be the number of binary strings of length n all of whose blocks have odd length.

(a) Determine a0 ,a1 ,a2 ,a3 .

(b) Find the generating function for an .

(c) Write down a recurrence equation for an .

Question 4. Solve the recurrence equation

an = 4an−1 − 5an−2 + 2an−3

with initial conditions a0 = a1 = 1 and a2 = 2.