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
Harvey P. Dale, Table of n, a(n) for n = 1..1000
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 linear recurrences with constant coefficients, signature (2, -1).
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-François Alcover, Jan 24 2019 *)
LinearRecurrence[{2, -1}, {0, 1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}, 60] (* Harvey P. Dale, Aug 21 2021 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Offset corrected by David Radcliffe, Apr 18 2016
STATUS
approved