A129606 - OEIS

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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A129606

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

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 10, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 24, 37, 42, 51, 25, 38, 26, 44, 47, 27, 53, 56, 60, 28, 39, 29, 43, 52, 30, 40, 31, 45, 46, 32, 48, 49, 50, 33, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 67, 68, 69, 107

(list; graph; refs; listen; history; text; internal format)

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.........B...D

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

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

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

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

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

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

Note that automorphism *A072796 = ENIPS(*A129606). See the definition given in A122204.

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 (*A129606 s) (cond ((> (length s) 2) (cons (caddr s) (cons (car s) (cons (cadr s) (cdddr s))))) (else (*A072796 s))))

(define (*A129606! s) (cond ((< (length s) 3) (*A072796! s)) (else (let ((org_car (car s))) (set-car! s (caddr s)) (set-car! (cddr s) (cadr s)) (set-car! (cdr s) org_car) s))))

CROSSREFS

Inverse: A129605.

Sequence in context: A364824 A062894 A339723 * A057510 A130920 A127285

Adjacent sequences: A129603 A129604 A129605 * A129607 A129608 A129609

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 22 2007

STATUS

approved