A154451 Signature permutation of a Catalan bijection induced by generator "b" of the rightward recursing instance of Basilica group wreath recursion: a = (1,b), b = s(1,a).

0, 1, 3, 2, 7, 8, 6, 4, 5, 18, 17, 20, 21, 22, 16, 19, 14, 9, 10, 15, 11, 12, 13, 49, 50, 48, 45, 46, 55, 54, 57, 58, 59, 61, 62, 63, 64, 47, 44, 53, 56, 60, 42, 51, 37, 23, 24, 38, 25, 26, 27, 43, 52, 39, 28, 29, 40, 30, 31, 32, 41, 33, 34, 35, 36, 143, 142, 146, 147, 148

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 rightmost tip of the tree along the 111... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154451 = psi(A154441), 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 (*A154451! s) (cond ((pair? s) (*A154449! (cdr s)) (*A069770! s))) s)

Crossrefs

Inverse: A154452. a(n) = A154453(A069768(n)) = A057163(A154455(A057163(n))). Cf. A069770, A154449.

Sequence in context: A122328 A082346 A069889 * A131000 A122351 A323710

Adjacent sequences: A154448 A154449 A154450 * A154452 A154453 A154454

Keyword

nonn

Author

Antti Karttunen, Jan 17 2009

Status

approved