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A246565 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly increasing. 2
1, 1, 2, 3, 6, 9, 20, 31, 67, 115, 238, 406, 880, 1494, 3118, 5568, 11408, 20092, 41938, 73687, 151529, 272359, 552611, 987277, 2033173, 3617167, 7371745, 13318869, 26991289, 48496985, 99264686, 177917588, 362349258, 655925568, 1331038563, 2401097768, 4913906801, 8844673793, 18046697901, 32720071992, 66666578597 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..40.

Joerg Arndt, All trees for 0 <= n <= 7

EXAMPLE

The a(4) = 6 such trees are:

:

:   1:

:  [ 1 1 1 1 ]

:  [ 0 0 0 0 ]

:

:  O--o

:  .--o

:  .--o

:  .--o

:

:

:   2:

:  [ 1 1 2 ]

:  [ 0 0 0 ]

:

:  O--o

:  .--o

:  .--o--o

:

:

:   3:

:  [ 1 3 ]

:  [ 0 0 ]

:

:  O--o

:  .--o--o--o

:

:

:   4:

:  [ 2 2 ]

:  [ 0 0 ]

:

:  O--o--o

:  .--o--o

:

:

:   5:

:  [ 2 2 ]

:  [ 0 1 ]

:

:  O--o--o

:     .--o--o

:

:

:   6:

:  [ 4 ]

:  [ 0 ]

:

:  O--o--o--o--o

:

See the Arndt link for all trees for 0 <= n <= 7.

CROSSREFS

Cf. A000108 (all trees), A246566 (descending branch lengths), A193196, A192243.

Sequence in context: A003243 A320160 A055873 * A320169 A293606 A185376

Adjacent sequences:  A246562 A246563 A246564 * A246566 A246567 A246568

KEYWORD

nonn

AUTHOR

Joerg Arndt, Aug 30 2014

STATUS

approved

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Last modified April 11 23:12 EDT 2021. Contains 342895 sequences. (Running on oeis4.)