A154450 Signature permutation of a Catalan bijection: The inverse of A154449.

0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 11, 9, 10, 15, 14, 16, 17, 18, 19, 20, 21, 22, 31, 32, 34, 35, 36, 30, 33, 28, 24, 23, 29, 25, 26, 27, 40, 41, 39, 37, 38, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 87, 88, 90, 91, 92, 96, 97

Offset

0,3

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 111... ray, but not starting swapping until at the right-hand side child of the root, leaving the root itself fixed. Specifically, *A154450 = psi(A154440), where the isomorphism psi is given in A153141 (see further comments there).

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154450! s) (if (pair? s) (*A154452! (cdr s))) s)

Crossrefs

Inverse: A154449. a(n) = A069767(A154456(n)) = A057163(A154454(A057163(n))). Cf. A069770, A154452.

Differs from A089850 for the first time at n=31, where a(31)=24, while A089850(31)=23.

Sequence in context: A130375 A154122 A089850 * A154449 A122304 A122303

Adjacent sequences: A154447 A154448 A154449 * A154451 A154452 A154453

Keyword

nonn

Author

Antti Karttunen, Jan 17 2009

Status

approved