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%I #6 Mar 31 2012 13:21:12
%S 0,1,2,3,4,6,5,8,7,9,11,14,16,19,10,15,13,21,22,12,20,17,18,23,25,28,
%T 30,33,37,39,42,44,47,51,53,56,60,24,29,38,43,52,27,41,35,58,59,36,62,
%U 63,64,26,40,34,57,61,31,54,45,46,32,55,48,49,50,65,67,70,72,75,79,81
%N Signature permutation of a Catalan automorphism: row 253 of table A122203.
%C This is the signature-permutation of Catalan automorphism which is derived from nonrecursive Catalan automorphism *A123503 with the recursion schema SPINE (defined in A122203).
%C The number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation begins as 1,1,2,1,3,1,4,1,8,1,16,1,47,..., the LCM of cycle sizes as 1,1,1,2,12,12,120,120,840,840,5040,5040,55440,... (cf. A089423) and the cycle-count sequence seems to be A045629. (To be proved.)
%D A. Karttunen, paper in preparation, draft available by e-mail.
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define *A123717! (!SPINE *A123503!))
%Y Inverse: A123718. a(n) = A057509(A089854(n)). Row 253 of A122203.
%K nonn
%O 0,3
%A _Antti Karttunen_, Oct 11 2006
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