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%I #8 Oct 15 2015 10:55:24
%S 0,1,3,2,8,7,5,6,4,22,20,21,18,17,13,12,15,19,16,10,11,14,9,64,61,62,
%T 55,54,63,57,59,50,49,58,46,48,45,36,34,35,32,31,41,40,52,60,53,43,56,
%U 47,44,27,26,29,33,30,38,39,51,42,24,25,28,37,23,196,192,193,181,180
%N Permutation of natural numbers induced by the Catalan bijection gma086428 acting on symbolless S-expressions encoded by A014486/A063171.
%C This Catalan bijection rotates by "half step" the interpretations (pp)-(rr) of Stanley, using the "descending slope" mapping illustrated in A086431.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (With the complete Scheme source)
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%Y Inverse: A086427. a(n) = A086431(A086427(A086431(n))) = A057164(A085174(A057164(n))) = A086425(A057502(A086426(n))). Occurs in A073200. Cf. also A086430 (whole step rotate).
%Y Number of cycles: A002995. Number of fixed points: A019590. Max. cycle size: A057543. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 23 2003