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

Author

Antti Karttunen, Apr 16 2002

Keywords

• nonn

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

• 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

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.