(defun robot (x y k)
  (let ((n 100) (m 100) (x1 60) (y1 60))
    (if (= k 0)
      (if (and (= x x1) (= y y1)) 1 0)
      (let
        (
          (up (if (< (+ y 1) m) (robot x (+ y 1) (- k 1)) 0))
          (down (if (>= (- y 1) 0) (robot x (- y 1) (- k 1)) 0))
          (right (if (< (+ x 1) n) (robot (+ x 1) y (- k 1)) 0))
          (left (if (>= (- x 1) 0) (robot (- x 1) y (- k 1)) 0))
        )
        (+ up down right left)
      )
    )
  )
)

(defun memoize (fn)
  (let ((cache (make-hash-table :test #'equal)))
    #'(lambda (&rest args)
        (multiple-value-bind
              (result exists)
            (gethash args cache)
          (if exists
              result
              (setf (gethash args cache)
                    (apply fn args)))))))

(setf (fdefinition 'robot) (memoize #'robot))

(print (robot 50 50 200))