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 A057509 Permutation of natural numbers: rotations of the bottom branches of the rooted plane trees encoded by A014486. 18
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 14 14:06 EDT 2019. Contains 328017 sequences. (Running on oeis4.)