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A126310
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A014486-index for the Dyck path "derived" from the n-th Dyck path encoded by A014486(n).
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3
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0, 0, 1, 0, 2, 1, 1, 1, 0, 4, 2, 2, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 0, 9, 4, 4, 4, 2, 4, 2, 4, 5, 2, 2, 2, 2, 1, 4, 2, 2, 2, 1, 4, 2, 6, 7, 3, 2, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 1, 1, 1, 1, 0, 23, 9, 9, 9, 4, 9, 4, 9, 10, 4, 4, 4, 4, 2, 9, 4, 4, 4, 2, 9, 4, 11, 12, 5, 4, 4, 5, 2, 4, 2, 4, 5, 2, 4, 5, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| According to Vaille, the concept of "derivation des ponts" is defined by Kreweras, in "Sur les eventails de segments" paper.
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REFERENCES
| G. Kreweras, Sur les eventails de segments, Cahiers du Bureau Universitaire de Recherche Operationelle, Cahier no. 15, Paris, 1970, pp. 3-41.
J. Vaill\'{e}, Une Bijection Explicative de Plusieurs Proprietes Remarquables des Ponts, European J. Combin. 18 (1997), no. 1, 117-124.
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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)))))
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CROSSREFS
| a(n) = A125986(A126309(A125985(n))).
Sequence in context: A120691 A111941 A153462 * A109086 A105794 A160380
Adjacent sequences: A126307 A126308 A126309 * A126311 A126312 A126313
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 02 2007
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