%I #5 Mar 31 2012 13:21:13
%S 0,1,2,3,4,6,5,7,8,9,11,14,16,19,10,15,12,17,18,13,20,21,22,23,28,25,
%T 30,33,37,39,42,44,47,51,53,56,60,24,29,38,43,52,26,40,31,45,46,32,48,
%U 49,50,27,41,34,54,55,35,57,58,59,36,61,62,63,64,65,70,79,84,93,67,81
%N Signature-permutation of a Catalan automorphism: ENIPS-transformation of *A057508.
%C ENIPS-transformation is explained in A122204. This automorphism permutes the top-level of a list of even length (1 ... 2n) as (2 4 6 ... 2n-2 2n 2n-1 2n-3 ... 5 3 1) and when applied to a list of odd length (1 .. 2n+1), permutes it as (2 4 6 ... 2n-2 2n 2n+1 2n-1 2n-3 ... 5 3 1). Used to construct A127288.
%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 (*A127286! s) (cond ((pair? s) (*A127286! (cdr s)) (*A057508! s))) s)
%Y Inverse: A127285. a(n) = A057508(A127288(n)).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007