%I #9 Jun 27 2012 13:51:05
%S 0,1,3,2,7,6,8,5,4,17,16,18,15,14,20,19,22,12,11,21,13,10,9,45,44,46,
%T 43,42,48,47,50,40,39,49,41,38,37,54,53,55,52,51,61,60,63,31,30,62,32,
%U 29,28,57,56,64,34,33,59,36,26,25,58,35,27,24,23,129,128,130,127,126
%N Permutation of natural numbers induced by the Catalan Automorphism *A074683 acting on parenthesizations as encoded and ordered by A014486/A063171
%C 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.
%C This is a rare example of Catalan Automorphism (with simple definition) where the cycle count sequence (A089411) is not monotone. (See A127296 for more complex example.)
%H A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme function implementing this automorphism on list-structures/S-expressions:) (define (*A074683! s) (cond ((pair? s) (*A074683! (car s)) (*A074683! (cdr s)) (*A074679! s))) s)
%Y Row 12 of A122202. Inverse of A074684. a(n) = A057163(A074682(A057163(n))).
%Y 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.
%K nonn
%O 0,3
%A _Antti Karttunen_, Sep 11 2002
|