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A127379
Signature-permutation of Callan's 2006 bijection on Dyck Paths, mirrored version (A057164-conjugate).
7
0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 13, 12, 14, 15, 19, 22, 21, 16, 20, 17, 18, 23, 24, 25, 27, 26, 28, 29, 33, 36, 35, 30, 34, 31, 32, 37, 38, 39, 41, 40, 51, 52, 60, 64, 63, 56, 62, 58, 59, 42, 43, 53, 54, 55, 44, 61, 45, 46, 47, 57, 48, 50, 49, 65, 66, 67, 69, 68, 70, 71
OFFSET
0,3
COMMENTS
It's much easier to implement Callan's 2006 bijection for S-expressions if one considers a mirror-image of the graphical description given by Callan (on page 3). Then this automorphism is just RIBS-transformation (explained in A122200) of the automorphism A127377 and Callan's original variant A127381 is obtained as A057164(a(A057164(n))).
PROG
(Scheme implementation of this automorphism, destructive, that acts on S-expressions, i.e. list-structures:)
(define (*A127379! s) (for-each *A127377! s) s)
CROSSREFS
Inverse: A127380. a(n) = A057164(A127381(A057164(n))). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127384 and A086625 shifted once right. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, ... A127302(a(n)) = A127302(n) holds for all n. A127388 shows a variant which is an involution.
Differs from A073289 and A122349 for the first time at n=54, where a(n)=54, while A073289(54) = A122349(54) = 61.
Sequence in context: A122350 A127381 A085169 * A073289 A122349 A127388
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 16 2007
STATUS
approved