

A127377


Signaturepermutation of a Catalan automorphism, auxiliary bijection for Callan's 2006 bijection on Dyck Paths.


7



0, 1, 3, 2, 8, 7, 6, 4, 5, 22, 21, 20, 17, 18, 14, 15, 19, 9, 10, 16, 11, 13, 12, 64, 63, 62, 58, 59, 54, 55, 61, 45, 46, 57, 48, 50, 49, 37, 38, 39, 41, 40, 51, 52, 60, 23, 24, 56, 25, 27, 26, 42, 43, 53, 28, 29, 44, 33, 36, 35, 47, 30, 34, 31, 32, 196, 195, 194, 189, 190
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OFFSET

0,3


COMMENTS

Used to construct A127379.


LINKS

A. Karttunen, Table of n, a(n) for n = 0..2055
Index entries for signaturepermutations of Catalan automorphisms


PROG

(Scheme implementation of this automorphism, destructive, that acts on Sexpressions, i.e. liststructures:)
(define (*A127377! s) (cond ((null? s)) ((null? (car s)) (*A069770! s) (*A127377! (car s))) ((null? (cdr s)) (*A069770! s) (*A127379! (cdr s))) (else (*A127379! s))) s)


CROSSREFS

Inverse: A127378. The number of cycles and the number of fixed points in range [A014137(n1)..A014138(n1)] of this permutation are given by A127383 and A127389. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, ... A127387 shows a variant which is an involution. A127302(a(n)) = A127302(n) holds for all n.
Sequence in context: A154457 A073292 A073297 * A069768 A122301 A086425
Adjacent sequences: A127374 A127375 A127376 * A127378 A127379 A127380


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jan 16 2007


STATUS

approved



