|
Search: id:A057510
|
|
|
| A057510 |
|
Permutation of natural numbers: rotations of the bottom branches of the rooted plane trees encoded by A014486. (to opposite direction of A057509). |
|
+0
16
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
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)
|
|
PROGRAM
|
(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: A121730 A062894 A129606 this_sequence A130920 A127285 A130945
Adjacent sequences: A057507 A057508 A057509 this_sequence A057511 A057512 A057513
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Antti Karttunen Sep 03 2000
|
|
|
Search completed in 0.002 seconds
|
