1) Write a function that uses recursion that converts a decimal number to octal (base 8). The function should accept a single integer and return a String containing the base 8 equivalent.

2) Write a recursive function that implement the following functions:

a. x⁰ = 1
xⁿ = x * x^n-1 if n > 0

b. x⁰ = 1
xⁿ = (x^n/2)² if n > 0 and n is even
xⁿ = x * (x^n/2)² if n> 0 and n is odd

3) How many multiplications will the functions you wrote in problem #2 perform when computing 3¹⁹? 3³²?
How many recursive calls will the functions make when computing 3¹⁹? 3³²?

4) Write a recursive function that implements the following function:

f(1) = 1; f(2) = 1; f(3) = 1; f(4) = 3; f(5) = 5
f(n) = f(n-1) + 3 * f(n-5) for all n > 5

Make the function as efficient as possible.

5) Compute f(n) for n = 6, 7, 12, 15