;;; This code needs to burrrrn
(proclaim '(optimize (speed 3) (space 0) (debug 0) (safety 0)
                     (compilation-speed 0)))

(defun bf-possi (n)
  (declare (fixnum n))
  (loop
    :for j fixnum :from 0 :to (floor n 2)
    :for n2-next-fac integer :from (- (* -4 n) 10) :by 8
    ;V  (n - 2j + 1)(n - 2j + 2)  V
    :for n-next-fac :of-type (integer 0 *) = (* (1+ n) (+ 2 n))
    :then (+ n2-next-fac n-next-fac)
    ;V            (n - 2j)         V
    ;V        n! 6                 V
    ;V  -------------------------  V
    ;V  (n - 2j)! (j!)^2  (j + 1)  V
    :for curr :of-type (integer 0 *) = (expt 6 n)
    :then (* curr (/ n-next-fac (* 36 j (1+ j))))
    :sum curr :of-type (integer 0 *)))

(defun bf-possi-for (n)
  (format t "Length: ~D  Possible BF Programs: ~D~%"
          n (bf-possi n)))

;;; Calculate all possible BF programs up to /top-n/
(defun bf-possi-to (top-n)
  (loop
    :for n :from 1 :to top-n :do
    (bf-possi-for n)))

(time (bf-possi-for 1000))