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%I #7 May 01 2014 02:48:29
%S 0,1,2,3,4,6,5,7,8,9,11,14,16,19,10,15,12,17,18,13,20,21,22,23,25,28,
%T 30,33,37,39,42,44,47,51,53,56,60,24,29,38,43,52,26,40,31,45,46,32,48,
%U 49,50,27,41,34,54,55,35,57,58,59,36,61,62,63,64,65,67,70,72,75,79,81
%N Permutation of natural numbers: rotations of the bottom branches of the rooted plane trees encoded by A014486.
%C The number of objects (rooted planar trees, mountain ranges, parenthesizations) fixed by this permutation can be computed with procedure fixedcount, which gives A034731.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme program for computing this sequence)
%p map(CatalanRankGlobal,map(RotateBottomBranchesL, A014486));
%p RotateBottomBranchesL := n -> pars2binexp(rotateL(binexp2pars(n)));
%p rotateL := proc(a) if 0 = nops(a) then (a) else [op(cdr(a)), a[1]]; fi; end;
%p fixedcount := proc(n) local d,z; z := 0; for d in divisors(n) do z := z+C(d-1); od; RETURN(z); end;
%o (Scheme function implementing this automorphism on list-structures:) (define (Rol s) (cond ((not (pair? s)) s) (else (append (cdr s) (list (car s))))))
%o (Destructive variant, see A057501 for RotateHandshakes! and swap!) (define (Rol! s) (cond ((pair? s) (swap! s) (RotateHandshakes! s))) s)
%Y Inverse of A057510 and the car/cdr-flipped conjugate of A069775 and also composition of A069770 & A057501, i.e. A057509(n) = A057163(A069775(A057163(n))) = A057501(A069770(n)).
%Y Cycle counts given by A003239. Cf. also A057511.
%K nonn
%O 0,3
%A _Antti Karttunen_, Sep 03 2000
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