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A057502
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Permutation of natural numbers: rotations of non-crossing handshakes encoded by A014486. (to opposite direction of A057501).
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29
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0, 1, 3, 2, 7, 6, 8, 4, 5, 17, 16, 18, 14, 15, 20, 19, 21, 9, 10, 22, 11, 12, 13, 45, 44, 46, 42, 43, 48, 47, 49, 37, 38, 50, 39, 40, 41, 54, 53, 55, 51, 52, 57, 56, 58, 23, 24, 59, 25, 26, 27, 61, 60, 62, 28, 29, 63, 30, 31, 32, 64, 33, 34, 35, 36, 129, 128, 130, 126, 127
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| In A057501 and A057502, the cycles between A014138[n-1]+1-th and A014138[n]th term partition A000108[n] objects encoded by the corresponding terms of A014486 into A002995[n+1] equivalence classes of planar trees, thus the latter sequence can be produced also with Maple procedure RotHandshakesPermutationCycleCounts given below.
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LINKS
| Index entries for sequences that are permutations of the natural numbers
A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)
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MAPLE
| map(CatalanRankGlobal, map(RotateHandshakesR, A014486));
RotateHandshakesR := n -> pars2binexp(deepreverse(RotateHandshakesP(deepreverse(binexp2pars(n)))));
deepreverse := proc(a) if 0 = nops(a) or list <> whattype(a) then (a) else [op(deepreverse(cdr(a))), deepreverse(a[1])]; fi; end;
with(group); CountCycles := b -> (nops(convert(b, 'disjcyc')) + (nops(b)-convert(map(nops, convert(b, 'disjcyc')), `+`)));
RotHandshakesPermutationCycleCounts := 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, RotateHandshakes(CatalanUnrank(n, r)))]; od; a := [op(a), CountCycles(b)]; od; RETURN(a); end;
# For other procedures, follow A057501.
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PROG
| (Scheme function implementing this automorphism on list-structures:) (define (RotateHandshakesInv! s) (cond ((not (pair? s))) ((not (pair? (cdr s))) (swap! s)) (else (RotateHandshakesInv! (cdr s)) (robl! s))) s)
(define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))
(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))
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CROSSREFS
| Inverse of A057501 and the car/cdr-flipped conjugate of A069774, i.e. A057502(n) = A057163(A069774(A057163(n))). Cf. also A057507, A057510, A057513, A069771, A069772.
Sequence in context: A139285 A080398 A082321 * A071656 A130963 A130930
Adjacent sequences: A057499 A057500 A057501 * A057503 A057504 A057505
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen Sep 03 2000
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