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A069772
Self-inverse 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
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 16 2002
STATUS
approved