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A330627 Number of non-isomorphic phylogenetic trees with n nodes. 2
0, 1, 1, 1, 2, 2, 4, 5, 9, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A phylogenetic tree is a series-reduced rooted tree whose leaves are (usually disjoint) sets. Each branching as well as each element of each leaf contributes to the number of nodes.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

Non-isomorphic representatives of the a(2) = 1 through a(9) = 9 trees (commas and outer brackets elided):

  1  12  123  1234    12345    123456     1234567      12345678

              (1)(2)  (1)(23)  (1)(234)   (1)(2345)    (1)(23456)

                               (12)(34)   (12)(345)    (12)(3456)

                               (1)(2)(3)  (1)(2)(34)   (123)(456)

                                          (1)((2)(3))  (1)(2)(345)

                                                       (1)(23)(45)

                                                       (1)((2)(34))

                                                       (1)(2)(3)(4)

                                                       (12)((3)(4))

CROSSREFS

Phylogenetic trees by number of labels are A005804, with unlabeled version A141268.

Balanced phylogenetic trees are A320154.

Cf. A000311, A000669, A001678, A004114, A005121, A007716, A048816, A060356, A330465, A330467, A330469.

Sequence in context: A007147 A230380 A127968 * A188541 A037026 A116651

Adjacent sequences:  A330624 A330625 A330626 * A330628 A330629 A330630

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 28 2019

STATUS

approved

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Last modified February 18 15:04 EST 2020. Contains 332019 sequences. (Running on oeis4.)