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%I #4 Mar 31 2012 13:21:18
%S 0,1,3,2,8,7,6,4,5,21,22,20,18,17,19,16,14,9,10,15,11,12,13,58,59,62,
%T 63,64,57,61,55,50,49,54,48,45,46,56,60,53,47,44,51,42,37,23,24,38,25,
%U 26,27,52,43,39,28,29,40,30,31,32,41,33,34,35,36,170,171,174,175,176
%N Signature-permutation of a Catalan bijection induced by wreath recursion a=s(b,c), b=s(c,a), c=(c,c), starting from state b.
%C This Catalan bijection is induced by the second generator of group 2861 mentioned on page 144 of "Classification of groups generated by 3-state automata over a 2-letter alphabet" paper. Specifically, *A154457 = psi(A154447), where the isomorphism psi is given in A153141 (see further comments there).
%H A. Karttunen, <a href="/A154457/b154457.txt">Table of n, a(n) for n = 0..2055</a>
%H Bondarenko, Grigorchuk, Kravchenko, Muntyan, Nekrashevych, Savchuk, Sunic, <a href="http://arxiv.org/abs/0803.3555">Classification of groups generated by 3-state automata over a 2-letter alphabet</a>, p. 144.
%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 (*A154457! s) (cond ((pair? s) (*A069770! s) (*A154458! (car s)))) s)
%Y Inverse: A154458. a(n) = A057163(A154458(A057163(n))).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 17 2009