integer-composition-by-sequence.scm

(use-modules (srfi srfi-1)
             (ice-9 pretty-print))

(define (sum ls)
  (if (null? ls)
      0
      (+ (car ls) (sum (cdr ls)))))

(define (sum2 ls)
  (apply + ls))

(define* (integer-composition-by-sequence i #:optional (step 1) (beg 0))
  (let B ((M `((,beg ,(+ beg step)))) (lsm (+ beg beg step)))
    (if (null? (car M))
        (cdr (reverse (cdr M)))
        (let ((nal (drop (car M) 1)))
          (let A ((al nal) (S (- lsm (caar M))))
            (cond
             ((null? al) (B (cons '() M) S)) ;; No solution
             ((< S i)
              (let* ((F (reverse al))
                     (Q (+ step (car F))))
                (A (reverse (cons Q F)) (+ S Q))))
             ((> S i)
              (A (cdr al) (- S (car al))))
             ((= S) (B (cons al M) S))))))))

(pretty-print
 (filter
  (lambda (l) (> (length (cdr l)) 1))
  (map (lambda (x) (cons x (integer-composition-by-sequence 216 x)))
       (iota 216 1))))