A154456 Signature permutation of a Catalan bijection: The inverse of A154455.

0, 1, 3, 2, 7, 8, 6, 4, 5, 17, 18, 20, 22, 21, 16, 19, 14, 9, 10, 15, 11, 12, 13, 45, 46, 48, 49, 50, 54, 55, 61, 63, 64, 57, 62, 58, 59, 44, 47, 53, 60, 56, 42, 51, 37, 23, 24, 38, 25, 26, 27, 43, 52, 39, 28, 29, 40, 30, 31, 32, 41, 33, 34, 35, 36, 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 descends along the 000... ray, starting swapping already at the root. Specifically, *A154456 = psi(A154446), 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 (*A154456! s) (cond ((pair? s) (*A069770! s) (*A154454! (car s)))) s)

Crossrefs

Inverse: A154455. a(n) = A069768(A154450(n)) = A057163(A154452(A057163(n))). Cf. A069770, A154454.

Differs from A082346 and A122328 for the first time at n=26, where a(26)=49, while A082346(26)=A122328(26)=50. Differs from A129611 for the first time at n=91, where a(91)=196, while A129611(91)=195.

Sequence in context: A154452 A130999 A129611 * A122328 A082346 A069889

Adjacent sequences: A154453 A154454 A154455 * A154457 A154458 A154459

Keyword

nonn

Author

Antti Karttunen, Jan 17 2009

Status

approved