0,3

This "gatomorphism" rotates car, cadr and cddr of an S-exp as (a . (b . c)) -> (b . (c . a)) if its length > 1, otherwise keeps it intact.

A. Karttunen, C-program for computing this sequence

Index entries for signature-permutations induced by Catalan automorphisms

(Scheme functions implementing this automorphism on list-structures:)

(define (gma089851! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) (else (swap! s) (robr! s) s)))

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

Inverse of A089853. a(n) = A089850(A072796(n)) = A057163(A089857(A057163(n))). Row 4 of A089840.

Number of cycles: A089847. Number of fixed-points: A089848. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A130381 A130948 A122343 this_sequence A122310 A122305 A131143

Adjacent sequences: A089848 A089849 A089850 this_sequence A089852 A089853 A089854

nonn

Antti Karttunen (Firstname.Surname(AT)iki.fi), Nov 29 2003