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A057509
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Permutation of natural numbers: rotations of the bottom branches of the rooted plane trees encoded by A014486.
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19
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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
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0,3
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COMMENTS
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The number of objects (rooted planar trees, mountain ranges, parenthesizations) fixed by this permutation can be computed with procedure fixedcount, which gives A034731.
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LINKS
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A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)
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MAPLE
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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;
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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