A129605 Signature-permutation of a Catalan automorphism, row 3613 of A089840.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 11, 14, 16, 19, 10, 15, 12, 17, 18, 13, 20, 21, 22, 23, 24, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 25, 29, 38, 43, 52, 26, 40, 31, 45, 46, 32, 48, 49, 50, 27, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 67, 68, 69, 79, 80

Offset

0,3

Comments

This involution effects the following transformation on the binary trees (labels A,B,C,D refer to arbitrary subtrees located on those nodes and () stands for a terminal node.)

.....C...D.........A...D

......\./...........\./

...B...X2........C...Y2......B..().......A..()

....\./...........\./.........\./.........\./

.A...X1....-->.B...Y1......A...X1..-->.B...Y1

..\./...........\./.........\./.........\./

...X0............Y0..........X0..........Y0

Note that automorphism *A072796 = SPINE(*A129605). See the definition given in A122203.

Links

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

A. Karttunen, Prolog-program which illustrates the construction of this and similar nonrecursive Catalan automorphisms.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Constructive and destructive Scheme implementation of this automorphism. These act on S-expressions, i.e. list-structures:)
(define (*A129605 s) (cond ((> (length s) 2) (cons (cadr s) (cons (caddr s) (cons (car s) (cdddr s))))) (else (*A072796 s))))
(define (*A129605! s) (cond ((< (length s) 3) (*A072796! s)) (else (let ((org_car (car s))) (set-car! s (cadr s)) (set-car! (cdr s) (caddr s)) (set-car! (cddr s) org_car) s))))

Crossrefs

Inverse: A129606.

Sequence in context: A130373 A121731 A244322 * A057509 A130919 A127286

Adjacent sequences: A129602 A129603 A129604 * A129606 A129607 A129608

Keyword

nonn

Author

Antti Karttunen, May 22 2007

Status

approved