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%I #11 Nov 18 2016 14:04:48
%S 0,1,3,2,7,8,6,4,5,18,17,20,21,22,16,19,14,9,10,15,11,12,13,49,50,48,
%T 45,46,55,54,57,58,59,61,62,63,64,47,44,53,56,60,42,51,37,23,24,38,25,
%U 26,27,43,52,39,28,29,40,30,31,32,41,33,34,35,36,143,142,146,147,148
%N Signature permutation of a Catalan bijection induced by generator "b" of the rightward recursing instance of Basilica group wreath recursion: a = (1,b), b = s(1,a).
%C 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 rightmost tip of the tree along the 111... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154451 = psi(A154441), where the isomorphism psi is given in A153141 (see further comments there).
%H A. Karttunen, <a href="/A154451/b154451.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154451! s) (cond ((pair? s) (*A154449! (cdr s)) (*A069770! s))) s)
%Y Inverse: A154452. a(n) = A154453(A069768(n)) = A057163(A154455(A057163(n))). Cf. A069770, A154449.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 17 2009