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%I #14 Mar 31 2012 14:02:27
%S 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,
%T 27,25,31,32,35,36,34,28,29,30,33,45,46,49,50,48,58,59,63,64,62,54,55,
%U 57,61,37,38,40,41,39,42,43,44,47,51,52,56,60,53,65,66,68,69,67
%N Permutation of natural numbers induced by Catalan Automorphism *A082356 acting on the parenthesizations encoded by A014486/A063171.
%C 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.
%H A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%o (Scheme function implementing this automorphism on S-expressions/list-structures:)
%o (define (*A082356! s) (cond ((pair? s) (*A082352! s) (*A082356! (car s)) (*A082356! (cdr s)))) s)
%Y Inverse of A082355. a(n) = A057163(A082358(n)). a(n) = A082364(A082853(n))+A082852(n). Cf. also A082351-A082352, A082357-A082358.
%Y Differs from A057117 first time at n=56: a(56)=42, while A057117(56)=44.
%K nonn
%O 0,3
%A _Antti Karttunen_, Apr 17 2003
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