%I #6 Mar 31 2012 13:21:14
%S 0,1,3,2,8,7,6,4,5,22,21,20,17,18,14,15,19,9,10,16,11,13,12,64,63,62,
%T 58,59,54,55,61,45,46,57,48,50,49,37,38,39,41,40,51,52,60,23,24,56,25,
%U 27,26,42,43,53,28,29,44,33,36,35,47,30,34,31,32,196,195,194,189,190
%N Signature-permutation of a Catalan automorphism, auxiliary bijection for Callan's 2006 bijection on Dyck Paths.
%C Used to construct A127379.
%H A. Karttunen, <a href="/A127377/b127377.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 (*A127377! s) (cond ((null? s)) ((null? (car s)) (*A069770! s) (*A127377! (car s))) ((null? (cdr s)) (*A069770! s) (*A127379! (cdr s))) (else (*A127379! s))) s)
%Y Inverse: A127378. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127383 and A127389. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, ... A127387 shows a variant which is an involution. A127302(a(n)) = A127302(n) holds for all n.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007