A082355 Permutation of natural numbers induced by Catalan Automorphism *A082355 acting on the parenthesizations encoded by A014486/A063171.

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

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.

Links

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

A. Karttunen, Catalan Automorphisms

Index entries for signature-permutations induced by Catalan automorphisms

Prog

(Scheme function implementing this automorphism on list-structures/S-expressions:)
(define (*A082355! s) (cond ((pair? s) (*A082355! (car s)) (*A082355! (cdr s)) (*A082351! s))) s)

Crossrefs

Inverse of A082356. a(n) = A082357(A057163(n)). a(n) = A082363(A082853(n))+A082852(n). Cf. also A082351-A082352, A082357-A082358.

Differs from A057118 first time at n=42: a(42)=56, while A057118(42)=58.

Sequence in context: A131150 A131153 A130993 * A057118 A122293 A130937

Adjacent sequences: A082352 A082353 A082354 * A082356 A082357 A082358

Keyword

nonn

Author

Antti Karttunen, Apr 17 2003

Status

approved