A057510 - OEIS

A057510

Permutation of natural numbers: rotations of the bottom branches of the rooted plane trees encoded by A014486. (to opposite direction of A057509).

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 10, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 37, 24, 42, 51, 25, 38, 26, 44, 47, 27, 53, 56, 60, 28, 39, 29, 43, 52, 30, 40, 31, 45, 46, 32, 48, 49, 50, 33, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 107, 66, 121, 149, 67

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..70.

Index entries for sequences that are permutations of the natural numbers

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

MAPLE

# reverse given in A057508, for CountCycles, see A057502, for other procedures, follow A057501.

map(CatalanRankGlobal, map(RotateBottomBranchesR, A014486));

RotateBottomBranchesR := n -> pars2binexp(rotateR(binexp2pars(n)));

rotateR := a -> reverse(rotateL(reverse(a)));

RotBBPermutationCycleCounts := proc(upto_n) local u, n, a, r, b; a := []; for n from 0 to upto_n do b := []; u := (binomial(2*n, n)/(n+1)); for r from 0 to u-1 do b := [op(b), 1+CatalanRank(n, RotateBottomBranchesL(CatalanUnrank(n, r)))]; od; a := [op(a), CountCycles(b)]; od; RETURN(a); end;

A003239 := RotBBPermutationCycleCounts(some_value); (e.g. 9. Cf. A057502, A057162)

PROG

(Scheme function implementing this automorphism on list-structures, see A057502 for RotateHandshakes! and swap!:) (define (Ror! s) (cond ((pair? s) (RotateHandshakesInv! s) (swap! s))) s)

CROSSREFS

Inverse of A057509 and the car/cdr-flipped conjugate of A069776 and also composition of A057502 & A069770, i.e. A057510(n) = A057163(A069776(A057163(n))) = A069770(A057502(n)).

Cycle counts given by A003239. Cf. also A057512, A057513.

Sequence in context: A062894 A339723 A129606 * A130920 A127285 A130945

Adjacent sequences: A057507 A057508 A057509 * A057511 A057512 A057513

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 03 2000

STATUS

approved