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

2,5

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

Table of n, a(n) for n=2..37.

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.

Sequence in context: A201542 A363251 A000672 * A115868 A103299 A278246

Adjacent sequences: A129857 A129858 A129859 * A129861 A129862 A129863

Keyword

nonn

Author

Barry Cipra, May 23 2007

Extensions

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

Status

approved