; f(n) = n, n < 3, f(n) = f(n-1) + 2f(n-2) + 3f(n-3) n >= 3

(define (f1 n)
  (if (< n 3)
      n
      (+ (f1 (- n 1))
	 (* 2 (f1 (- n 2)))
	 (* 3 (f1 (- n 3))))))

(define (f2 n)
  (if (< n 3)
      n
      (f-iter 2 1 0 n)))

; a = f(2), b = f(1), c = f(0)
; a <- a + 2b + 3c, b <- a, c <- b
(define (f-iter a b c count)
  (if (< count 3)
      a
      (f-iter (+ a (* 2 b) (* 3 c))
	      a
	      b
	      (- count 1))))