

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
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OFFSET

1,3


COMMENTS

Sleator et al. conjecture that a(n) = 2n6 for all n >= 11.
Lionel Pournin proved that a(n) = 2n6 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. 130137.
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, 13161355.
Lionel Pournin, The diameter of associahedra, arXiv:1207.6296 [math.CO], 20122014; Advances in Mathematics 259 (2014): 1342.
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, 647681.
Wikipedia, Tree rotation.
Index entries for sequences related to trees


FORMULA

a(n) = 2n6 for n >= 11.
From Chai Wah Wu, Feb 20 2018: (Start)
a(n) = 2*a(n1)  a(n2) 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] (* JeanFrançois 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



