OFFSET
0,5
COMMENTS
According to Vaillé, the concept of "dérivation des ponts" is defined by Kreweras, in "Sur les éventails de segments" paper.
LINKS
G. Kreweras, Sur les éventails de segments, Cahiers du Bureau Universitaire de Recherche Opérationelle, Cahier no. 15, Paris, 1970, pp. 3-41.
J. Vaillé, Une Bijection Explicative de Plusieurs Propriétés Remarquables des Ponts, European J. Combin. 18 (1997), no. 1, 117-124.
PROG
(MIT Scheme, function rising-list->binexp given in A125985): (define (A126310 n) (A080300 (rising-list->binexp (reverse! (map -1+ (map length (A126310-aux1 (A036044 (A014486 n)))))))))
(define (A126310-aux1 n) (let loop ((n n) (vs (list)) (u 0) (d 0)) (cond ((zero? n) (if (null? vs) vs (reverse! (cdr vs)))) ((= 2 (modulo n 4)) (loop (/ n 2) (cons (list (+ 1 u)) vs) (+ u 1) d)) ((= 1 (modulo n 4)) (add-valley-abscisses! (+ d 1) vs) (loop (/ (- n 1) 2) vs u (+ d 1))) ((odd? n) (loop (/ (- n 1) 2) vs u (+ d 1))) (else (loop (/ n 2) vs (+ u 1) d)))))
(define (add-valley-abscisses! valley-abscisse peak-ordonnees) (for-each (lambda (s) (append! s (list valley-abscisse))) (keep-matching-items peak-ordonnees (lambda (po) (>= (car po) valley-abscisse)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 02 2007
STATUS
approved