A074684 Permutation of natural numbers induced by Catalan Automorphism *A074684 acting on the parenthesizations encoded by A014486/A063171.

0, 1, 3, 2, 8, 7, 5, 4, 6, 22, 21, 18, 17, 20, 13, 12, 10, 9, 11, 15, 14, 19, 16, 64, 63, 59, 58, 62, 50, 49, 46, 45, 48, 55, 54, 61, 57, 36, 35, 32, 31, 34, 27, 26, 24, 23, 25, 29, 28, 33, 30, 41, 40, 38, 37, 39, 52, 51, 60, 56, 43, 42, 47, 44, 53, 196, 195, 190, 189, 194

Offset

0,3

Comments

This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184.

This is a rare example of a simply defined Catalan Automorphism where the cycle count sequence (A089411) is not monotone. (See A127296 for a much more complex example.)

Links

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

A. Karttunen, Catalan Automorphisms

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme function implementing this automorphism on list-structures/S-expressions:)
(define (*A074684! s) (cond ((pair? s) (*A074680! s) (*A074684! (car s)) (*A074684! (cdr s)))) s)

Crossrefs

Row 17 of A122201. Inverse of A074683. a(n) = A057163(A074681(A057163(n))).

The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in subpermutations limited by A014137 and A014138 are given by A089411, A086586 and A089412.

Sequence in context: A364390 A131172 A057503 * A131003 A082358 A130358

Adjacent sequences: A074681 A074682 A074683 * A074685 A074686 A074687

Keyword

nonn

Author

Antti Karttunen, Sep 11 2002

Status

approved