

A069772


Selfinverse permutation of natural numbers induced by the automorphism xReflectHandshakes acting on the parenthesizations encoded by A014486.


15



0, 1, 2, 3, 7, 6, 5, 4, 8, 9, 10, 21, 20, 19, 14, 15, 18, 17, 16, 13, 12, 11, 22, 45, 46, 44, 42, 43, 31, 32, 30, 28, 29, 63, 62, 61, 60, 54, 55, 53, 51, 52, 26, 27, 25, 23, 24, 59, 58, 57, 56, 40, 41, 39, 37, 38, 50, 49, 48, 47, 36, 35, 34, 33, 64, 65, 67, 66, 68, 69, 170
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

This automorphism reflects over the xaxis the interpretation n (the noncrossing handshakes) of Stanley's exercise 19.
Note that DeepRev (A057164) reflects over yaxis.
This transformation keeps palindromic parenthesizations/Dyck paths/rooted planar trees palindromic, but not necessarily same, meaning that this induces a permutation on the sequence A061855 (= A069766).


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 liststructures:) (define (xReflectHandshakes a) (DeepRev (RotateHandshakes180 a)))
(define (DeepRev lista) (cond ((not (pair? lista)) lista) ((null? (cdr lista)) (cons (DeepRev (car lista)) (list))) (else (append (DeepRev (cdr lista)) (DeepRev (cons (car lista) (list)))))))


CROSSREFS

Composition of A057164 and A069771 in either order, i.e. A069772(n) = A057164(A069771(n)) = A069771(A057164(n)). Cf. also A061855, A069766, A057501, A069888, A069889.
Sequence in context: A155891 A234026 A234612 * A098287 A115304 A098285
Adjacent sequences: A069769 A069770 A069771 * A069773 A069774 A069775


KEYWORD

nonn


AUTHOR

Antti Karttunen, Apr 16 2002


STATUS

approved



