A129860 Number of unrooted bifurcating tree shapes with n leaves.

1, 1, 1, 1, 2, 2, 4, 6, 11, 18, 37, 66, 135, 265, 552, 1132, 2410, 5098, 11020, 23846, 52233, 114796, 254371, 565734, 1265579, 2841632, 6408674, 14502229, 32935002, 75021750, 171404424, 392658842, 901842517, 2076217086, 4790669518, 11077270335

Offset: 2

Author

Barry Cipra, May 23 2007

Keywords

• nonn

Comments

Alternatively, the number of unrooted, unlabeled binary tree topologies with n leaves. - Steven Kelk, Jul 22 2016

This sequence is identical to A000672 (3-valent trees, boron trees, or binary trees) except the offset is different. A000672 is the main entry for this sequence and has much more information (including a b-file with many more terms). Thanks to Steven Kelk for noticing the errors in the present sequence (which have now been corrected), and for discovering the connection with A000672. - N. J. A. Sloane, Jul 22 2016

References

• Joseph Felsenstein, Inferring Phylogenies. Sinauer Associates, Inc., 2004, page 33. Note that at least the first two editions give an incorrect version of this sequence.

Links

• Jean-François Fortin, Wen-Jie Ma, Witold Skiba, Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond, arXiv:2006.13964 [hep-th], 2020.
• Jean-François Fortin, Wen-Jie Ma, Witold Skiba, All Global One- and Two-Dimensional Higher-Point Conformal Blocks, arXiv:2009.07674 [hep-th], 2020.

Crossrefs

Essentially the same sequence as A000672.

Extensions

Entry revised by N. J. A. Sloane, Jul 22 2016 at the suggestion of Steven Kelk