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%I #5 Mar 31 2012 13:21:14
%S 0,1,2,3,4,5,6,8,7,9,10,11,13,12,14,15,19,21,22,16,20,18,17,23,24,25,
%T 27,26,28,29,33,35,36,30,34,32,31,37,38,39,41,40,51,52,56,58,59,60,62,
%U 64,63,42,43,53,54,55,47,61,49,50,44,57,48,46,45,65,66,67,69,68,70,71
%N Signature-permutation of the inverse of Callan's 2006 bijection on Dyck Paths, mirrored version (A057164-conjugate).
%C This automorphism is RIBS-transformation (explained in A122200) of the automorphism A127378 and Callan's original variant A127382 is obtained as A057164(A127380(A057164(n))).
%H D. Callan, <a href="http://www.stat.wisc.edu/~callan/papers/Motzkin_manifestation/">A Bijection on Dyck Paths and Its Cycle Structure</a>, 2006, 17pp.
%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 (*A127380! s) (for-each *A127378! s) s)
%Y Inverse: A127379. a(n) = A057164(A127382(A057164(n))). A127302(a(n)) = A127302(n) holds for all n.
%Y Differs from A073288 for the first time at n=49, where a(n)=64, while A073288(49)=63 and differs from A122350 for the first time at n=54, where a(n)=54, while A122350(54)=57.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007