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%I #5 Mar 31 2012 13:21:13
%S 0,1,2,3,4,5,6,7,8,9,11,10,12,13,14,15,16,17,18,19,20,21,22,23,28,24,
%T 30,33,25,29,26,31,32,27,34,35,36,37,39,38,40,41,42,43,44,45,46,47,48,
%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,79,67,84,93,66,80
%N Signature-permutation of a Catalan automorphism: composition of A127285 and A057508.
%C This automorphism permutes the top-level of a list of even length (1 ... 2n) as (1 2n 2 2n-1 3 2n-3 ... n n+1) and when applied to a list of odd length (1 .. 2n+1), permutes it as (1 2n+1 2 2n 3 2n-1 ... n n+1). Used to construct A127291.
%H A. Karttunen, <a href="/A127287/b127287.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 (*A127287! s) (*A127285! (*A057508! s)))
%Y Inverse: A127288. a(n) = A127285(A057508(n)).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007
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