(define (f-recursive n)
  (if (< n 3) n
      (+ (f-recursive (- n 1))
         (* 2 (f-recursive (- n 2)))
         (* 3 (f-recursive (- n 3))))))

(define (f-iterative n)
  ; a = f(i - 2)
  ; b = f(i - 1)
  ; c = f(i)
  (define (iterate i a b c)
    (if (= i n) c
        (iterate (+ i 1)
                   b
                   c
                   (+ c
                      (* 2 b)
                      (* 3 a)))))
  (if (< n 3) n
      (iterate 2 0 1 2)))

(define (f-iterative-2 n)
  ; a = f(n - i)
  ; b = f(n - i + 1)
  ; c = f(n - i + 2)
  ; Note: n is not used as a state variable
  (define (iterate i a b c)
    (if (= i 2) c
        (iterate (- i 1)
                   b
                   c
                   (+ c
                      (* 2 b)
                      (* 3 a)))))
  (if (< n 3) n
      (iterate n 0 1 2)))