

A089857


Permutation of natural numbers induced by Catalan Automorphism *A089857 acting on the binary trees/parenthesizations encoded by A014486/A063171.


14



0, 1, 2, 3, 4, 5, 8, 6, 7, 9, 10, 11, 12, 13, 21, 22, 19, 14, 15, 20, 16, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 58, 59, 62, 63, 64, 56, 60, 51, 37, 38, 52, 39, 40, 41, 57, 61, 53, 42, 43, 54, 44, 45, 46, 55, 47, 48, 49, 50, 65, 66, 67, 68, 69, 70, 71, 72
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OFFSET

0,3


COMMENTS

.A...B...........C...A
..\./.............\./
...x...C....>....x...B...............()..A.........()..A..
....\./.............\./.................\./....>....\./...
.....x...............x...................x.............x....
((a . b) . c) > ((c . a) . b) _____ (() . a) > (() . a)
In terms of Sexpressions, this automorphism rotates caar, cdar and cdr of an Sexp, i.e., if carside is not ().
See the Karttunen OEISWiki link for a detailed explanation how to obtain a given integer sequence from this definition.


LINKS

Table of n, a(n) for n=0..72.
A. Karttunen, Catalan Automorphisms
A. Karttunen, Cprogram for computing this sequence
Index entries for signaturepermutations induced by Catalan automorphisms


PROG

(Scheme functions implementing this automorphism on liststructures/Sexpressions, both constructive (*A089857) and destructive (*A089857!) versions:)
(define (*A089857 s) (if (and (pair? s) (pair? (car s))) (cons (cons (cdr s) (caar s)) (cdar s)) s))
(define (*A089857! s) (cond ((not (pair? s)) s) ((not (pair? (car s))) s) (else (swap! s) (robl! s) s)))
(define (swap! s) (let ((excar (car s))) (setcar! s (cdr s)) (setcdr! s excar) s))
(define (robl! s) (let ((excar (car s))) (setcar! s (cddr s)) (setcdr! (cdr s) excar) (swap! (cdr s)) (swap! s) s))


CROSSREFS

Row 11 of A089840. Inverse of A089855. a(n) = A074679(A069770(n)) = A069770(A089862(n)) = A057163(A089851(A057163(n))).
Number of cycles: A089847. Number of fixedpoints: A089848 (in each range limited by A014137 and A014138).
Sequence in context: A082351 A122319 A123714 * A122316 A130990 A131150
Adjacent sequences: A089854 A089855 A089856 * A089858 A089859 A089860


KEYWORD

nonn


AUTHOR

Antti Karttunen, Nov 29 2003


EXTENSIONS

Further comments and constructive implementation of Schemefunction (*A089857) added by Antti Karttunen, Jun 04 2011


STATUS

approved



