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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Martin R. Smith

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A335408 Diameter of nearest neighbor interchange distance for free 3-trees.

Original entry on oeis.org

0, 1, 3, 5, 7, 10, 12, 15, 18, 21
Offset: 3

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Author

Martin R. Smith, Jun 06 2020

Keywords

Comments

a(n) is the maximum value of the nearest neighbor interchange distance between two unrooted binary trees with n leaves, obtained by evaluating the distance from one tree with each of the unlabeled n-leaf tree shapes (see A000672) to each labeled n-leaf tree (A001147) using the C script described in Li et al. (1996).
The known terms a(3),...,a(12) happen (coincidentally?) to match the first ten terms of A211266. However, it seems unlikely that the sequences will agree for ever.

References

  • Ming Li, John Tromp, and Louxin Zhang, Some notes on the nearest neighbour interchange distance, in Goos, G., Hartmanis, J., Leeuwen, J., Cai, J.-Y., and Wong, C. K., eds., "Computing and Combinatorics" 1090, Springer (Berlin, Heidelberg) (1996), 343-351. doi:10.1007/3-540-61332-3_168.

Links

Crossrefs

Cf. A211266, which happens to have the same initial terms (offset by two). It is not clear whether this correspondence continues for higher terms.
A000672 gives the number of unrooted tree shapes on n leaves; A001147 gives the number of (labeled) unrooted trees.

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