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%I #7 Jan 13 2013 06:14:38
%S 0,1,2,3,7,5,6,4,8,9,14,21,18,13,10,15,20,17,12,19,16,11,22,45,54,31,
%T 26,40,44,53,30,25,39,63,59,50,36,46,55,32,27,41,42,51,28,23,37,62,58,
%U 49,35,43,52,29,24,38,61,57,48,34,60,56,47,33,64,65,79,107,121,149,170
%N Self-inverse permutation of natural numbers induced by the automorphism RotateHandshakes180 acting on the parenthesizations encoded by A014486.
%C This automorphism rotates by 180 degrees the interpretation n (the non-crossing handshakes) of Stanley's exercise 19.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme program for computing this sequence)
%H R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catalan.pdf">Exercises on Catalan and Related Numbers</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme function implementing this automorphism on list-structures:) (define (RotateHandshakes180 a) (RotateHandshakes_n_steps a (count-pars a)))
%o (define (count-pars a) (if (not (pair? a)) 0 (+ 1 (count-pars (car a)) (count-pars (cdr a)))))
%o (define (RotateHandshakes a) (if (null? a) (list) (append (car a) (list (cdr a)))))
%o (define (RotateHandshakes_n_steps a n) (if (zero? n) a (RotateHandshakes_n_steps (RotateHandshakes a) (-1+ n))))
%Y Cf. A057501, A069772, A069888, A069889.
%K nonn
%O 0,3
%A Antti Karttunen, Apr 16 2002
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