A057509 - OEIS

A057509

Permutation of natural numbers: rotations of the bottom branches of the rooted plane trees encoded by A014486.

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, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 24, 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, 67, 70, 72, 75, 79, 81

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OFFSET

0,3

COMMENTS

The number of objects (rooted planar trees, mountain ranges, parenthesizations) fixed by this permutation can be computed with procedure fixedcount, which gives A034731.

LINKS

Table of n, a(n) for n=0..71.

Index entries for sequences that are permutations of the natural numbers

A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)

MAPLE

map(CatalanRankGlobal, map(RotateBottomBranchesL, A014486));

RotateBottomBranchesL := n -> pars2binexp(rotateL(binexp2pars(n)));

rotateL := proc(a) if 0 = nops(a) then (a) else [op(cdr(a)), a[1]]; fi; end;

fixedcount := proc(n) local d, z; z := 0; for d in divisors(n) do z := z+C(d-1); od; RETURN(z); end;

PROG

(Scheme function implementing this automorphism on list-structures:) (define (Rol s) (cond ((not (pair? s)) s) (else (append (cdr s) (list (car s))))))

(Destructive variant, see A057501 for RotateHandshakes! and swap!) (define (Rol! s) (cond ((pair? s) (swap! s) (RotateHandshakes! s))) s)

CROSSREFS

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)).

Cycle counts given by A003239. Cf. also A057511.

Sequence in context: A121731 A244322 A129605 * A130919 A127286 A130946

Adjacent sequences: A057506 A057507 A057508 * A057510 A057511 A057512

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 03 2000

STATUS

approved