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A082335 Permutation of natural numbers induced by the Catalan bijection gma082335 acting on the parenthesizations encoded by A014486/A063171. 7
0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 13, 12, 22, 11, 10, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 36, 35, 59, 34, 32, 31, 60, 61, 62, 33, 30, 63, 29, 27, 26, 64, 28, 25, 24, 23, 107, 108, 109, 110, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This Catalan bijection rotates binary trees left, if possible, otherwise reflects them with the Catalan bijection A057163.

LINKS

Table of n, a(n) for n=0..69.

A. Karttunen, Gatomorphisms (with the complete Scheme source)

Index entries for signature-permutations induced by Catalan automorphisms

PROG

(Scheme functions implementing this automorphism on list-structures:)

(define (gma082335! s) (cond ((pair? s) (cond ((pair? (cdr s)) (robl! s)) (else (gma057163! s))))) s)

(define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))

(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))

CROSSREFS

Inverse of A082336. Cf. also A074679-A074680, A082349-A082350.

Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A123695 A123499 A082349 * A074690 A122332 A074685

Adjacent sequences:  A082332 A082333 A082334 * A082336 A082337 A082338

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 17 2003

STATUS

approved

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)