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A154455 Signature permutation of a Catalan bijection induced by generator "b" of the leftward recursing instance of Basilica group wreath recursion: a = (b,1), b = s(a,1).

%I A154455 #4 Mar 31 2012 13:21:17
%S A154455 0,1,3,2,7,8,6,4,5,17,18,20,21,22,16,19,14,9,10,15,11,13,12,45,46,48,
%T A154455 49,50,54,55,57,58,59,61,62,63,64,44,47,53,56,60,42,51,37,23,24,38,25,
%U A154455 26,27,43,52,39,28,29,41,33,35,36,40,30,34,31,32,129,130,132,133,134
%N A154455 Signature permutation of a Catalan bijection induced by generator "b" of the leftward recursing instance of Basilica group wreath recursion: a = (b,1), b = s(a,1).
%C A154455 This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the leftmost tip of the tree along the 000... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154455 = psi(A154445), where the isomorphism psi is given in A153141 (see further comments there).
%H A154455 A. Karttunen, <a href="/A154455/b154455.txt">Table of n, a(n) for n = 0..2055</a>
%H A154455 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o A154455 (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154455! s) (cond ((pair? s) (*A154453! (car s)) (*A069770! s))) s)
%Y A154455 Inverse: A154456. a(n) = A154449(A069767(n)) = A057163(A154451(A057163(n))). Cf. A069770, A154453.
%Y A154455 Differs from A082345 for the first time at n=49, where a(49)=26, while A082345(49)=27. Differs from A122327 for the first time at n=26, where a(26)=49, while A122327(26)=50. Differs from A129612 for the first time at n=195, where a(195)=92, while A129612(195)=91.
%K A154455 nonn
%O A154455 0,3
%A A154455 _Antti Karttunen_, Jan 17 2009