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%I #4 Mar 31 2012 13:21:18
%S 0,1,3,2,7,8,6,5,4,17,18,20,21,22,16,19,15,13,12,14,11,9,10,45,46,48,
%T 49,50,54,55,57,58,59,61,62,63,64,44,47,53,56,60,43,52,41,35,36,40,34,
%U 32,31,42,51,39,33,30,37,28,23,24,38,29,25,26,27,129,130,132,133,134
%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 a.
%C This Catalan bijection is induced by the first generator of group 2861 mentioned on page 144 of "Classification of groups generated by 3-state automata over a 2-letter alphabet" paper. Specifically, *A154458 = psi(A154448), where the isomorphism psi is given in A153141 (see further comments there).
%H A. Karttunen, <a href="/A154458/b154458.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 (*A154458! s) (cond ((pair? s) (*A069770! s) (*A154457! (cdr s)))) s)
%Y Inverse: A154457. a(n) = A057163(A154457(A057163(n))).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 17 2009
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