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A085159 Permutation of natural numbers induced by the Catalan bijection gma085159 acting on symbolless S-expressions encoded by A014486/A063171. 10
0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 11, 14, 16, 19, 17, 20, 12, 10, 13, 21, 15, 18, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 45, 48, 54, 57, 61, 31, 34, 26, 24, 27, 35, 29, 32, 36, 58, 62, 40, 38, 41, 49, 43, 46, 50, 63, 52, 55, 59, 64, 65, 67, 70, 72, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "rising slope" mapping illustrated in A085161.
LINKS
A. Karttunen, Gatomorphisms (With the complete Scheme source)
R. P. Stanley, Exercises on Catalan and Related Numbers (including 66 combinatorial interpretations)
PROG
(Scheme functions implementing this automorphism on list-structures:)
(define (gma085159 s) (cond ((null? s) s) (else (app-to-xrt (car s) (append (cdr s) (list (list)))))))
CROSSREFS
Inverse: A085160. a(n) = A085161(A085160(A085161(n))) = A085169(A082315(A085170(n))) = A074684(A082315(A074683(n))) = A085173(A085173(n)). Occurs in A073200. Cf. also A085165-A085168, A086429. Scheme-function app-to-xrt given in A085203.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
Sequence in context: A073196 A086430 A073194 * A085171 A085163 A084469
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 23 2003
STATUS
approved

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)