A069772 Self-inverse permutation of natural numbers induced by the automorphism xReflectHandshakes acting on the parenthesizations encoded by A014486.

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

Offset

0,3

Comments

This automorphism reflects over the x-axis the interpretation n (the non-crossing handshakes) of Stanley's exercise 19.

Note that DeepRev (A057164) reflects over y-axis.

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 list-structures:) (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: A245443 A246265 A234612 * A277819 A098287 A115304

Adjacent sequences: A069769 A069770 A069771 * A069773 A069774 A069775

Keyword

nonn

Author

Antti Karttunen, Apr 16 2002

Status

approved