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 A125986 Signature-permutation of the inverse of Vaille's 1997 bijection on Dyck paths. 10
 0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 19, 20, 15, 14, 21, 17, 18, 13, 11, 16, 12, 10, 9, 64, 60, 61, 52, 51, 62, 54, 55, 41, 39, 53, 40, 38, 37, 63, 57, 58, 46, 44, 59, 49, 50, 36, 33, 47, 34, 29, 28, 56, 45, 48, 35, 31, 43, 32, 27, 25, 42, 30, 26, 24, 23, 196, 191, 192, 178, 177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES J. Vaill\'{e}, Une Bijection Explicative de Plusieurs Proprietes Remarquables des Ponts, European J. Combin. 18 (1997), no. 1, 117-124. LINKS A. Karttunen, Table of n, a(n) for n = 0..2055 PROG (MIT Scheme:) (define (A125986 n) (let ((z (reduce append! '() (reverse! (descending-list->bin-lists (binexp->A071158-list (A014486 n)))))) (tl (A057515 n))) (A080300 (/ (+ (<< (- (<< 1 tl) 1) (+ (length z) 1)) (binlist->n z)) 2)))) (define (descending-list->bin-lists rl) (let loop ((z (list)) (m 1)) (let ((sl (map (lambda (n) (- n m)) (keep-matching-items rl (lambda (n) (or (= n m) (= n (+ 1 m)))))))) (cond ((null? sl) z) (else (loop (cons sl z) (+ m 1))))))) (define (binlist->n binlist) (let loop ((s 0) (bl binlist)) (if (null? bl) s (loop (+ s s (car bl)) (cdr bl))))) (define (binexp->A071158-list n) (let loop ((n n) (lista (list)) (h 1)) (cond ((zero? n) lista) ((odd? n) (loop (/ (- n 1) 2) lista (- h 1))) (else (loop (/ n 2) (cons h lista) (1+ h)))))) (define (>> n i) (if (zero? i) n (>> (floor->exact (/ n 2)) (- i 1)))) (define (<< n i) (if (<= i 0) (>> n (- i)) (<< (+ n n) (- i 1)))) CROSSREFS Inverse: A125985. Cf. A057515, A071158. Algorithm is partially described in A126301. Sequence in context: A071667 A057506 A086427 * A131155 A085174 A131164 Adjacent sequences:  A125983 A125984 A125985 * A125987 A125988 A125989 KEYWORD nonn AUTHOR Antti Karttunen, Jan 02 2007 STATUS approved

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