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%I #5 Mar 31 2012 13:21:14
%S 0,1,2,3,4,5,6,8,7,9,10,11,13,12,14,15,19,22,21,16,20,18,17,23,24,25,
%T 27,26,28,29,33,36,35,30,34,32,31,37,38,39,41,40,51,52,60,64,63,56,62,
%U 59,58,42,43,53,54,55,47,61,50,49,44,57,48,46,45,65,66,67,69,68,70,71
%N Signature-permutation of a Catalan automorphism, a self-inverse variant of A127379.
%C This automorphism is RIBS-transformation (explained in A122200) of the automorphism A127387.
%H A. Karttunen, <a href="/A127388/b127388.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 implementation of this automorphism, destructive, that acts on S-expressions, i.e. list-structures:)
%o (define (*A127388! s) (for-each *A127387! s) s)
%Y The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this involution are given by A127386 and A086625 shifted once right (this automorphism has the same fixed points as A127379/A127380). A127302(a(n)) = A127302(n) holds for all n.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007