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A129860
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Number of unrooted bifurcating tree shapes with n leaves.
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6
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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
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OFFSET
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2,5
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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CROSSREFS
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Essentially the same sequence as A000672.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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