A082356 Permutation of natural numbers induced by Catalan Automorphism *A082356 acting on the parenthesizations encoded by A014486/A063171.

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

Offset

0,3

Comments

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

Differs from A057117 first time at n=56: a(56)=42, while A057117(56)=44.

Links

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

A. Karttunen, Catalan Automorphisms

Index entries for signature-permutations induced by Catalan automorphisms

Formula

a(n) = A057163(A082358(n)).

a(n) = A082364(A082853(n)) + A082852(n).

Prog

(Scheme) ;; Function implementing this automorphism on S-expressions/list-structures:
(define (*A082356! s) (cond ((pair? s) (*A082352! s) (*A082356! (car s)) (*A082356! (cdr s)))) s)

Crossrefs

Inverse of A082355.

Cf. A057163, A082351, A082352, A082357, A082358.

Cf. A057177.

Sequence in context: A122294 A130349 A130354 * A057117 A130941 A082360

Adjacent sequences: A082353 A082354 A082355 * A082357 A082358 A082359

Keyword

nonn

Author

Antti Karttunen, Apr 17 2003

Status

approved