project euler 65

pe_65.clj

;; Problem 65  : 2011/11/25
;; "Elapsed time: 3.193423 msecs"

(defn cf-seq-of-e [n]
  (cond (zero? n) 2
	(= (rem n 3) 2) (* 2 (/ (inc n) 3))
	:else 1))

(defn-memo cf-numerator [n a-seq]
  (cond (zero? n) 1
	(= 1 n) (a-seq 0)
	:else (+ (* (a-seq (dec n))
		    (cf-numerator (dec n) a-seq))
		 (cf-numerator (- n 2) a-seq))))

(defn-memo cf-denominator [n a-seq]
  (cond (zero? n) 0
	(= 1 n) 1
	:else (+ (* (a-seq (dec n))
		    (cf-denominator (dec n) a-seq))
		 (cf-denominator (- n 2) a-seq))))

(defn pe-65 [n]
  (sum-of-digits (cf-numerator n cf-seq-of-e)))