A130923 Signature permutation of a Catalan automorphism: Inverse FORK-transform of automorphism *A120705.

0, 1, 3, 2, 7, 8, 5, 4, 6, 17, 18, 20, 21, 22, 12, 11, 13, 9, 10, 15, 14, 16, 19, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 31, 32, 29, 28, 30, 34, 33, 35, 27, 24, 36, 23, 26, 25, 40, 39, 41, 37, 38, 43, 42, 44, 47, 52, 51, 53, 56, 60, 129, 130, 132, 133, 134

Offset

0,3

Comments

This is the unique Catalan automorphism f, such that *A120705 = (FORK f). See A122201 for the definition of FORK.

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme) ;; Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:
(define (*A130923! s) (cond ((pair? s) (*A120705! s) (*A120706! (car s)) (*A120706! (cdr s)))) s)
(Scheme) ;; Another version where the call to car-branch is eliminated, but cdr-branch gets just more complex:
(define (*A130923! s) (cond ((pair? s) (*A074680! s) (cond ((pair? (cdr s)) (*A120705! (cddr s)) (*A120706! (cadr s)) (*A120706! (cdr s)))))) s)

Crossrefs

Inverse: A130924. Cf. A130925 & A130926.

Sequence in context: A130394 A130955 A129610 * A057501 A071655 A130964

Adjacent sequences: A130920 A130921 A130922 * A130924 A130925 A130926

Keyword

nonn

Author

Antti Karttunen, Jun 11 2007

Status

approved