

A154454


Signature permutation of a Catalan bijection: The inverse of A154453.


6



0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 19, 21, 22, 16, 20, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 51, 52, 56, 58, 59, 60, 62, 64, 63, 42, 43, 53, 57, 61, 44, 54, 45, 46, 47, 55, 48, 49, 50, 65, 66, 67, 68, 69, 70, 71
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, but not starting swapping until at the lefthand side child of the root, leaving the root itself fixed. Specifically, *A154454 = psi(A154444), 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 signaturepermutations of Catalan automorphisms


PROG

(Scheme function, destructive implementation of this automorphism acting on Sexpressions:) (define (*A154454! s) (if (pair? s) (*A154456! (car s))) s)


CROSSREFS

Inverse: A154453. a(n) = A069768(A154452(n)) = A057163(A154450(A057163(n))). Cf. A069770, A154456.
Differs from its inverse A154453 for the first time at n=49, where a(49)=64, while A154454(49)=63. Differs from A089854 for the first time at n=49, where a(49)=64, while A089854(49)=63. Differs from A131173 for the first time at n=26, where a(26)=26, while A131173(26)=27.
Sequence in context: A089866 A089854 A154453 * A131173 A073286 A122312
Adjacent sequences: A154451 A154452 A154453 * A154455 A154456 A154457


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jan 17 2009


STATUS

approved



