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A005152 Rotation distance between binary trees on n nodes.
(Formerly M0963)
1
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; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

REFERENCES

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).

LINKS

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

FORMULA

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)

MATHEMATICA

a[n_] := If[n < 11, {0, 1, 2, 4, 5, 7, 9, 11, 12, 15}[[n]], 2n - 6]; Array[a, 53] (* Jean-Fran├žois Alcover, Jan 24 2019 *)

CROSSREFS

Sequence in context: A049039 A325101 A301728 * A060831 A073727 A075692

Adjacent sequences:  A005149 A005150 A005151 * A005153 A005154 A005155

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Offset corrected by David Radcliffe, Apr 18 2016

STATUS

approved

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)