A246565 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly increasing.

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

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