;;; hw02-problem1.ss
;;; Comp210, 98.spring
;;;
;;; Functions for problem 1 -- determine how many
;;; recursive calls are made (using Donkey), for 0 <= n <= 6.
;;;


;; fact: num -> num
;; Return n!, which stands for n*(n-1)*(n-2)*...*3*2*1
;;
(define fact
  (lambda (n)
    (if (zero? n)
        1
        (* n (fact (- n 1))))))

;; multfib: num -> num
;; A multiplicative version of the fibonacci sequence.
;;
(define multfib
  (lambda (n)
    (if (< n 3)
        n
        (* (multfib (- n 1))
           (multfib (- n 2))))))

;; threes: num -> num
;; Returns 1???
;;
(define threes
  (lambda (n)
    (if (< n 2)
        1
        (threes (if (even? n)
                    (/ n 2)
                    (+ 1 (* n 3)))))))