A154455 Signature permutation of a Catalan bijection induced by generator "b" of the leftward recursing instance of Basilica group wreath recursion: a = (b,1), b = s(a,1).

0, 1, 3, 2, 7, 8, 6, 4, 5, 17, 18, 20, 21, 22, 16, 19, 14, 9, 10, 15, 11, 13, 12, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 44, 47, 53, 56, 60, 42, 51, 37, 23, 24, 38, 25, 26, 27, 43, 52, 39, 28, 29, 41, 33, 35, 36, 40, 30, 34, 31, 32, 129, 130, 132, 133, 134

Offset

0,3

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the leftmost tip of the tree along the 000... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154455 = psi(A154445), 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 (*A154455! s) (cond ((pair? s) (*A154453! (car s)) (*A069770! s))) s)

Crossrefs

Inverse: A154456. a(n) = A154449(A069767(n)) = A057163(A154451(A057163(n))). Cf. A069770, A154453.

Differs from A082345 for the first time at n=49, where a(49)=26, while A082345(49)=27. Differs from A122327 for the first time at n=26, where a(26)=49, while A122327(26)=50. Differs from A129612 for the first time at n=195, where a(195)=92, while A129612(195)=91.

Sequence in context: A154126 A069770 A129612 * A082345 A122327 A154452

Adjacent sequences: A154452 A154453 A154454 * A154456 A154457 A154458

Keyword

nonn

Author

Antti Karttunen, Jan 17 2009

Status

approved