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

Author

Antti Karttunen, Jan 17 2009

Keywords

• nonn

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

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.