Homework Problems Mat 331

Set no. 2 October 17, 2003

Due October 24, 2003

1. Write a procedure to generate the Fibonacci numbers, which are defined by

   $$F(n)= \begin{cases}F(n-1)+F(n-2), &\text{if $ n>2$;}\ 1, &\text{if $ n=1$ or $n=2$} \end{cases}$$

   
   

   We implemented the recursive procedure in class (see worksheets Oct17.mws). Implement a non-recursive procedure.

2. The Irby numbers are defined by

   $$I(n)= \begin{cases}I(n-9)+I(n-10), &\text{if $ n>10$;}\\ n, &\text{if $0\leq n \leq 10$} \end{cases}$$

   
   
   • Implement a recursive procedure.
   • Implement a non-recursive procedure.