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Signature-permutation of a Catalan automorphism: SPINE-transformation of *A057508.
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%I #5 Mar 31 2012 13:21:13

%S 0,1,2,3,4,6,5,7,8,9,14,10,16,19,11,15,12,17,18,13,20,21,22,23,37,25,

%T 42,51,24,38,26,44,47,27,53,56,60,28,39,29,43,52,30,40,31,45,46,32,48,

%U 49,50,33,41,34,54,55,35,57,58,59,36,61,62,63,64,65,107,70,121,149,66

%N Signature-permutation of a Catalan automorphism: SPINE-transformation of *A057508.

%C SPINE-transformation is explained in A122203. This automorphism permutes the top-level of a list of even length (1 ... 2n) as (2n 1 2n-1 2 2n-3 3 ... n+1 n) and when applied to a list of odd length (1 .. 2n+1), permutes it as (2n+1 1 2n 2 2n-1 3 ... n n+1). Used to construct A127287 and A127289.

%H A. Karttunen, <a href="/A127285/b127285.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 (*A127285! s) (cond ((pair? s) (*A057508! s) (*A127285! (cdr s)))) s)

%Y Inverse: A127286. a(n) = A127287(A057508(n)).

%K nonn

%O 0,3

%A _Antti Karttunen_, Jan 16 2007