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 A069771 Self-inverse permutation of natural numbers induced by the automorphism RotateHandshakes180 acting on the parenthesizations encoded by A014486. 10
 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, 26, 40, 44, 53, 30, 25, 39, 63, 59, 50, 36, 46, 55, 32, 27, 41, 42, 51, 28, 23, 37, 62, 58, 49, 35, 43, 52, 29, 24, 38, 61, 57, 48, 34, 60, 56, 47, 33, 64, 65, 79, 107, 121, 149, 170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This automorphism rotates by 180 degrees the interpretation n (the non-crossing handshakes) of Stanley's exercise 19. LINKS A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence) R. P. Stanley, Exercises on Catalan and Related Numbers PROG (Scheme function implementing this automorphism on list-structures:) (define (RotateHandshakes180 a) (RotateHandshakes_n_steps a (count-pars a))) (define (count-pars a) (if (not (pair? a)) 0 (+ 1 (count-pars (car a)) (count-pars (cdr a))))) (define (RotateHandshakes a) (if (null? a) (list) (append (car a) (list (cdr a))))) (define (RotateHandshakes_n_steps a n) (if (zero? n) a (RotateHandshakes_n_steps (RotateHandshakes a) (-1+ n)))) CROSSREFS Cf. A057501, A069772, A069888, A069889. Sequence in context: A318739 A205299 A222242 * A235801 A076986 A225403 Adjacent sequences:  A069768 A069769 A069770 * A069772 A069773 A069774 KEYWORD nonn AUTHOR Antti Karttunen, Apr 16 2002 STATUS approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)