0,3

This gatomorphism swaps the two leftmost branches of the general plane trees if the degree of the root > 1, and keeps the tree intact if it is planted (root's degree = 1). Together with the gatomorphism A069770 it is used to recursively compose the whole infinite sequence of gatomorphisms of simple type B given in the array A073200.

A. Karttunen, Table of n, a(n) for n = 0..196

A. Karttunen, Gatomorphisms (with the complete Scheme source)

Index entries for sequences that are permutations of the natural numbers

(Scheme function implementing this automorphism on list-structures, first the constructive variant:)

(define (gmA072796 s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) (else (cons (cadr s) (cons (car s) (cddr s))))))

(THEN the destructive variant:)

(define (gmA072796! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) (else (swap! s) (robr! s) (swap! (cdr s)) s)))

(define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))

(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))

Row 2 of A089840.

The car/cdr-flipped conjugate of A072797, i.e. A072796(n) = A057163(A072797(A057163(n))). Occurs for first time in A073200 as row 1. Fixed point counts and cycle counts are given in A073190 and A073191.

Sequence in context: A130340 A130339 A058812 this_sequence A130374 A122363 A122364

Adjacent sequences: A072793 A072794 A072795 this_sequence A072797 A072798 A072799

nonn

Antti Karttunen Jun 12 2002