A082335 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A082335

Permutation of natural numbers induced by the Catalan bijection gma082335 acting on the parenthesizations encoded by A014486/A063171.

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