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%I #5 Mar 31 2012 13:21:12
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,21,19,20,18,22,23,24,25,
%T 26,27,28,29,30,31,35,33,34,32,36,37,38,39,40,41,42,43,44,45,58,56,54,
%U 49,63,51,52,53,48,62,47,57,46,59,60,61,55,50,64,65,66,67,68,69,70,71
%N An involution of nonnegative integers: signature permutation of Catalan automorphism which is obtained with recursion schema RIBS from automorphism *A085161
%C Recursion schema RIBS is defined in A122200. Number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation is given by INVERT transform of A001405, appropriately shifted.
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Scheme function, constructive implementation of this automorphism acting on S-expressions:) (define *A123719 (RIBS *A085161))
%Y a(n) = A085160(A085163(n)). A085163(n) = A085159(a(n)).
%K nonn
%O 0,3
%A _Antti Karttunen_, Oct 11 2006