A069771 Self-inverse permutation of natural numbers induced by the automorphism RotateHandshakes180 acting on the parenthesizations encoded by A014486.

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

Offset

0,3

Comments

This automorphism rotates by 180 degrees the interpretation n (the non-crossing handshakes) of Stanley's exercise 19.

Links

Table of n, a(n) for n=0..70.

A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)

R. P. Stanley, Exercises on Catalan and Related Numbers

Index entries for sequences that are permutations of the natural 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 * A330423 A235801 A076986

Adjacent sequences: A069768 A069769 A069770 * A069772 A069773 A069774

Keyword

nonn

Author

Antti Karttunen, Apr 16 2002

Status

approved