A082354 Permutation of natural numbers induced by the Catalan bijection gma082354 acting on the parenthesizations encoded by A014486/A063171.

0, 1, 2, 3, 6, 4, 5, 7, 8, 14, 15, 16, 9, 10, 19, 11, 12, 17, 18, 13, 20, 21, 22, 37, 38, 39, 40, 41, 42, 43, 44, 23, 24, 47, 25, 26, 27, 51, 52, 53, 28, 29, 56, 30, 31, 45, 46, 32, 48, 49, 50, 60, 33, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 107, 108, 109, 110, 111

Offset

0,3

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 (gma082354! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) ((not (pair? (cddr s))) (swap! (robl! s))) (else (robl! 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 A082353. a(n) = A057163(A082352(A057163(n))).

Sequence in context: A157248 A368229 A085515 * A130344 A122344 A130382

Adjacent sequences: A082351 A082352 A082353 * A082355 A082356 A082357

Keyword

nonn

Author

Antti Karttunen, Apr 17 2003

Status

approved