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Search: id:A057161
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| A057161 |
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Permutation of natural numbers induced by counter-clockwise rotation of the triangularizations of polygons encoded by A014486. |
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13
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| 0, 1, 3, 2, 7, 8, 5, 6, 4, 17, 18, 20, 21, 22, 12, 13, 15, 16, 19, 10, 11, 14, 9, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 31, 32, 34, 35, 36, 40, 41, 43, 44, 47, 52, 53, 56, 60, 26, 27, 29, 30, 33, 38, 39, 42, 51, 24, 25, 28, 37, 23, 129, 130, 132, 133, 134
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..2055
A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)
Illustration of triangulations of polygons.
Index entries for sequences that are permutations of the natural numbers
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MAPLE
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a(n) = CatalanRankGlobal(RotateTriangularization(A014486[n]))
CatalanRankGlobal given in A057117 and the other Maple procedures in A038776.
NextSubBinTree := proc(nn) local n, z, c; n := nn; c := 0; z := 0; while(c < 1) do z := 2*z + (n mod 2); c := c + (-1)^n; n := floor(n/2); od; RETURN(z); end;
BinTreeLeftBranch := n -> NextSubBinTree(floor(n/2));
BinTreeRightBranch := n -> NextSubBinTree(floor(n/(2^(1+binwidth(BinTreeLeftBranch(n))))));
RotateTriangularization := proc(nn) local n, s, z, w; n := binrev(nn); z := 0; w := 0; while(1 = (n mod 2)) do s := BinTreeRightBranch(n); z := z + (2^w)*s; w := w + binwidth(s); z := z + (2^w); w := w + 1; n := floor(n/2); od; RETURN(z); end;
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PROGRAM
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(Scheme function implementing this automorphism on list-structures:) (define (RotateTriangularization bt) (let loop ((lt bt) (nt (list))) (cond ((not (pair? lt)) nt) (else (loop (car lt) (cons (cdr lt) nt))))))
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CROSSREFS
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Inverse of A057162 and also its car/cdr-flipped conjugate, composition of A069769 & A069767, i.e. A057161(n) = A057163(A057162(A057163(n))) = A069767(A069769(n)).
Cf. also A057163, A057164, A057501, A057505. Max cycle lengths: A057544.
Adjacent sequences: A057158 A057159 A057160 this_sequence A057162 A057163 A057164
Sequence in context: A130396 A131010 A071657 this_sequence A130363 A089862 A125981
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Aug 18 2000
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