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A129605 Signature-permutation of a Catalan automorphism, row 3613 of A089840. 3
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 (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.........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

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Last modified November 14 12:20 EST 2019. Contains 329114 sequences. (Running on oeis4.)