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A005152
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Rotation distance between binary trees on n nodes.
(Formerly M0963)
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1
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0, 1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
(list;
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OFFSET
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1,3
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COMMENTS
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Sleator et al. conjecture that a(n) = 2n-6 for all n >= 11.
Lionel Pournin proved that a(n) = 2n-6 for all n >= 11. - David Radcliffe, Apr 18 2016
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REFERENCES
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D. D. Sleator, R. E. Tarjan and W. P. Thurston, Rotation distance, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 130-137.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..53.
Patrick Dehornoy, On the rotation distance between binary trees, Adv. Math. 223 (2010), no. 4, 1316-1355.
Lionel Pournin, The diameter of associahedra, arXiv:1207.6296 [math.CO], 2012-2014; Advances in Mathematics 259 (2014): 13-42.
Daniel D. Sleator, Email to N. J. A. Sloane, May 15 1991.
Daniel D. Sleator, Robert E. Tarjan, William P. Thurston, Rotation distance, triangulations and hyperbolic geometry, J. Amer. Math. Soc. 1 (1988), no. 3, 647-681.
Wikipedia, Tree rotation.
Index entries for sequences related to trees
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FORMULA
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a(n) = 2n-6 for n >= 11.
From Chai Wah Wu, Feb 20 2018: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 12.
G.f.: x*(x^11 - 2*x^10 + 2*x^9 - x^8 + x^5 - x^4 + x^3 + x)/(x - 1)^2. (End)
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MATHEMATICA
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a[n_] := If[n < 11, {0, 1, 2, 4, 5, 7, 9, 11, 12, 15}[[n]], 2n - 6]; Array[a, 53] (* Jean-François Alcover, Jan 24 2019 *)
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CROSSREFS
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Sequence in context: A049039 A325101 A301728 * A060831 A073727 A075692
Adjacent sequences: A005149 A005150 A005151 * A005153 A005154 A005155
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Offset corrected by David Radcliffe, Apr 18 2016
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STATUS
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approved
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