Coin Partitions

p78.lisp

@@ -0,0 +1,20 @@
+;; Memoized computation via recurrence relation
+(let ((memo (make-hash-table)))
+  (defun partition-count (n)
+    (or (gethash n memo)
+	(setf (gethash n memo)
+	      (cond ((= n 0) 1)
+		    ((< n 0) 0)
+		    (t 
+		     (flet ((lower-bound (n) (ceiling (- (/ (- (sqrt (+ (* 24 n) 1)) 1) 6))))
+			    (upper-bound (n) (/ (+ (sqrt (+ (* 24 n) 1)) 1) 6)))
+		       (loop for k from (lower-bound n) upto (upper-bound n)
+			     unless (= k 0)
+			       sum (* (expt -1 (1+ k))
+				      (partition-count (- n (* k (/ (- (* 3 k) 1) 2)))))))))))))
+
+(defun coin-partitions (&optional (divisor 1000000))
+  (loop for n upfrom 2
+	for p = (partition-count n)
+	until (= (mod p divisor) 0)
+	finally (return n)))