Converting to a HOP-style iterator left as an exercise. 

(defn lazy-triangle 
  ([]
    (cons [1] (lazy-triangle [1])))
  ([row]
    (let [pairs (partition 2 1 row)
          next-row (concat [1] (map #(apply + %) pairs) [1])]
      (lazy-seq (cons (vec next-row) (lazy-triangle next-row))))))
;;
;; user=> (pprint (take 10 (lazy-triangle)))
;; ([1]
;;  [1 1]
;;  [1 2 1]
;;  [1 3 3 1]
;;  [1 4 6 4 1]
;;  [1 5 10 10 5 1]
;;  [1 6 15 20 15 6 1]
;;  [1 7 21 35 35 21 7 1]
;;  [1 8 28 56 70 56 28 8 1]
;;  [1 9 36 84 126 126 84 36 9 1])
;;

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The cake is a lie.
The cake is a lie.

In reply to Re: problem in my sub partition by Fletch
in thread problem in my sub partition by PhillipHuang

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