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A125986
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Signature-permutation of the inverse of Vaille's 1997 bijection on Dyck paths.
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10
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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
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OFFSET
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0,3
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REFERENCES
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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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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..2055
Index entries for signature-permutations of Catalan automorphisms
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PROG
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(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))))
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jan 02 2007
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STATUS
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approved
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