login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126313 Signature-permutation of a Catalan automorphism: composition of A069772 and A125976. 10
0, 1, 3, 2, 8, 5, 6, 4, 7, 22, 13, 15, 12, 14, 19, 21, 16, 11, 18, 10, 20, 17, 9, 64, 36, 41, 35, 40, 52, 53, 38, 34, 39, 55, 51, 37, 54, 60, 63, 32, 62, 31, 56, 59, 47, 33, 50, 27, 58, 49, 26, 43, 44, 29, 61, 30, 24, 57, 48, 25, 46, 42, 28, 23, 45, 196, 106, 120, 105, 119 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Like A069771, A069772, A125976 and A126315/A126316, this automorphism keeps symmetric Dyck paths symmetric, but not necessarily same.
LINKS
CROSSREFS
Inverse: A126314. a(n) = A069772(A125976(n)) = A126290(A069772(n)) = A126315(A057164(n)). The number of cycles, number of fixed points, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127277, A127278, A127279 and A127280. The fixed points are given by A127306. Note the curiosity: this automorphism partitions the A000108(8) = 1430 Catalan structures of size eight (e.g. Dyck paths of length 16) into 79 equivalence classes, of which the largest contains 79 members.
Sequence in context: A072788 A085178 A146942 * A125979 A071663 A071664
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 16 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)