(defun make-tree (depth)
  (make-array (- (expt 2 depth) 1)))

(defun root (tree)
  (cons 0 tree))


(defun index-of-level (l) (- (expt 2 l) 1))
(defun width-of-level (l) (expt 2 l))
(defun level-of-node  (n) (truncate (log (+ n 1) 2)))
(defun offset-of-node (n) (- n (index-of-level (level-of-node n))))

(defun print-examples ()
  (loop for n below 32 do (format t "~3D ~3D ~3D ~3D ~3D~%"
                                  n
                                  (offset-of-node n)
                                  (level-of-node n)
                                  (index-of-level (level-of-node n))
                                  (width-of-level (level-of-node n)))))


(defun (setf data) (new-data node) (setf (aref (cdr node) (car node)) new-data))
(defun data  (node)        (aref (cdr node) (car node)))
(defun child (node child)  (+ child (* 2 (offset-of-node node)) (index-of-level (+ 1 (level-of-node node)))))
(defun left  (node) (cons (child (car node) 0) (cdr node)))
(defun right (node) (cons (child (car node) 1) (cdr node)))

(let* ((tree (make-tree 3))
       (root (root tree)))
  (setf (data (left  (left  root))) 0
        (data        (left  root))  1
        (data (right (left  root))) 2
        (data               root)   3
        (data (left  (right root))) 4
        (data        (right root))  5
        (data (right (right root))) 6)
  tree)

--> #(3 1 5 0 2 4 6)