The Pascal Triangle in Clojure

pascal_triangle.clj

;; The Pascal Triangle: https://www.hackerrank.com/challenges/pascals-triangle/problem?isFullScreen=true

;; For a given integer , print the first  rows of Pascal's Triangle. 
;; Print each row with each value separated by a single space. 
;; The value at the row and  column of the triangle is equal to where indexing starts from. 
;; These values are the binomial coefficients.

;; The Pascal Triangle
;; 1
;; 1 1
;; 1 2 1
;; 1 3 3 1
;; 1 4 6 4 1

;; ....
;; Input Format
;; A single line of input, integer `K`.

;; Constraints
;; 2 <= `K` <= 10

;; Output Format
;; Output the first `K` rows of Pascal's triangle.

;; Sample Input
;; 4

;; Sample Output
;; 1
;; 1 1
;; 1 2 1
;; 1 3 3 1

;; Sample Input
;; 7

;; Sample Output
;; 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

(defn triangle
  [input & {:keys [row output]
            :or {row 1 output []}}]
  
  (defn append [seq & {:keys [to] :or {to []}}]
    (conj to seq))
  
  (defn form-seq [seq]
    (flatten [(first seq) (form-rest seq)]))

  (defn form-rest
    [input-seq & {:keys [column output]
                  :or {column 1 output []}}]

    (let [sum-seq (+ (or (first input-seq) 0)
                     (or (second input-seq) 0))
          seq (flatten (list (append sum-seq :to output)))]
      (if (empty? input-seq)
        (drop-last seq)
        (form-rest (nthrest input-seq 1)
                   :column (inc column)
                   :output (vec seq)))))
  
  (let [seq (cond (or (<= input 1) (= row 1)) '(1)
                  :else (form-seq (last output)))]
    (cond
      (<= input 1)
      (append seq :to output)

      (= row 1)
      (triangle input
                :row (inc row)
                :output (append seq :to output))

      (< row input)
      (triangle input
                :row (inc row)
                :output (append seq :to output))

      :else
      (append seq :to output))))

(doseq [row (triangle 10)]
  (apply prn row))

;; 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



;; for hackerrank submission: https://www.hackerrank.com/challenges/pascals-triangle/problem?isFullScreen=true

; Enter your code here. Read input from STDIN. Print output to STDOUT
;

(let [i (read-string (read-line))]
  (defn append [seq & {:keys [to] :or {to []}}]
    (conj to seq))

  (defn form-rest
    [input-seq & {:keys [column output]
                  :or {column 1 output []}}]

    (let [sum-seq (+ (or (first input-seq) 0)
                     (or (second input-seq) 0))
          seq (flatten (list (append sum-seq :to output)))]
      (if (empty? input-seq)
        (drop-last seq)
        (form-rest (nthrest input-seq 1)
                   :column (inc column)
                   :output (vec seq)))))

  (defn form-seq [seq]
    (flatten [(first seq) (form-rest seq)]))

  (defn triangle
    [input & {:keys [row output]
              :or {row 1 output []}}]

    (let [seq (cond (or (<= input 1) (= row 1)) '(1)
                    :else (form-seq (last output)))]
      (cond
        (<= input 1)
        (append seq :to output)

        (= row 1)
        (triangle input
                  :row (inc row)
                  :output (append seq :to output))

        (< row input)
        (triangle input
                  :row (inc row)
                  :output (append seq :to output))

        :else
        (append seq :to output))))

  (doseq [row (triangle i)]
    (apply prn row)))