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A129604 Signature-permutation of a Catalan automorphism, row 1654720 of A089840. 5
0, 1, 3, 2, 8, 7, 6, 5, 4, 21, 22, 20, 17, 18, 19, 16, 15, 12, 13, 14, 11, 9, 10, 58, 59, 62, 63, 64, 57, 61, 54, 45, 46, 55, 48, 49, 50, 56, 60, 53, 44, 47, 52, 43, 40, 31, 32, 41, 34, 35, 36, 51, 42, 39, 30, 33, 37, 28, 23, 24, 38, 29, 25, 26, 27, 170, 171, 174, 175, 176 (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.)

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

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

...x...x....-->..x...x.......()..x..-->..x..()........x..()...-->..()..x..

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

.....x.............x...........x...........x............x............x....

Note that automorphism *A069770 = FORK(*A129604) = KROF(*A129604). See the definitions given in A122201 and A122202.

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 (*A129604 s) (cond ((pair? s) (cons (*A069770 (cdr s)) (*A069770 (car s)))) (else s)))

(define (*A129604! s) (cond ((pair? s) (*A069770! (car s)) (*A069770! (cdr s)) (*A069770! s))) s)

CROSSREFS

a(n) = A069770(A089864(n)) = A089864(A069770(n)). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this involution are given by the same sequences as is the case for example with A069770, A057163 and A122351, that is, A007595 and zero-interspersed A000108.

Sequence in context: A122354 A131160 A276622 * A130359 A122340 A082347

Adjacent sequences:  A129601 A129602 A129603 * A129605 A129606 A129607

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 22 2007

STATUS

approved

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Last modified November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)