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%I #5 Mar 31 2012 13:21:16
%S 0,1,2,3,4,6,5,7,8,9,11,14,16,19,10,15,12,17,18,13,20,21,22,23,25,28,
%T 30,33,37,39,42,44,47,51,53,56,60,24,29,38,43,52,26,40,31,45,54,32,46,
%U 49,50,27,41,34,48,55,35,57,58,62,36,61,59,63,64,65,67,70,72,75,79,81
%N Signature permutation of a Catalan automorphism: DEEPEN-transform of automorphism *A057511.
%C *A130919 = DEEPEN(*A057511) = NEPEED(*A057511) = DEEPEN(DEEPEN(*A057509)) = NEPEED(NEPEED(*A057509)). See A122283, A122284 for the definitions of DEEPEN and NEPEED transforms.
%H A. Karttunen, <a href="/A130919/b130919.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>
%Y Inverse: A130920. A122351(n) = A083927(A130919(A057123(n))). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130967 and A130968. Maximum cycle sizes seems to be given by A000793 (shifted once right).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 11 2007
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