all-bin-trees.clj

(defn queue
  [& c]
  (into
    (clojure.lang.PersistentQueue/EMPTY)
    c))

(defn k-combos 
  [k r]
  (if (zero? k) nil
    (letfn
      [(expand 
         [s]
         (let [i (peek s)]
           (into
             (pop s)
             (for [j (range (last i) r)]
               (conj i j)))))       
       (step 
         [s]
         (when-not
           (empty? s)
           (if (= 
                 (count
                   (peek s))
                 k)
             (cons
               (peek s)
               (lazy-seq
                 (step (pop s))))
             (lazy-seq
               (step (expand s))))))]
      (step 
        (into 
          (queue) 
          (map 
            vector 
            (range r)))))))


;tree:
;[ [2] [0 1] [1] [2] [1 1] ...]

(defn expand-tree 
  [t]
  (for [c 
        (rest
          (k-combos 
            (reduce + (last t))
            3))]
    (conj t c)))

(def all-trees
  (letfn
    [(step 
       [s]
       (when-not
         (empty? s)
         (cons
           (peek s)
           (lazy-seq
             (step
               (into
                 (pop s)
                 (expand-tree
                   (peek s))))))))]
    (step
      (queue [[1]] [[2]]))))