A246566 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly decreasing.

1, 1, 2, 4, 10, 24, 62, 155, 396, 992, 2504, 6228, 15512, 38220, 94059, 229498, 558642, 1350384, 3255138, 7801327, 18642118, 44329833, 105111283, 248184255, 584396849, 1371048495, 3208318247, 7483522231, 17413665881, 40405120865, 93543352492

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Joerg Arndt, All trees for 0 <= n <= 5

Example

The a(3) = 4 such trees are:
:
:     1:
:    [ 1 1 1 ]
:    [ 0 0 0 ]
:
:  O--o
:  .--o
:  .--o
:
:
:     2:
:    [ 2 1 ]
:    [ 0 0 ]
:
:  O--o--o
:  .--o
:
:
:     3:
:    [ 2 1 ]
:    [ 0 1 ]
:
:  O--o--o
:     .--o
:
:
:     4:
:    [ 3 ]
:    [ 0 ]
:
:  O--o--o--o
:
See the Arndt link for all trees for 0 <= n <= 5.

Crossrefs

Cf. A000108 (all trees), A246565 (ascending branch lengths), A193196, A192243, A001519.

Sequence in context: A006575 A307900 A230551 * A230553 A138175 A121691

Adjacent sequences: A246563 A246564 A246565 * A246567 A246568 A246569

Keyword

nonn

Author

Joerg Arndt, Aug 30 2014

Status

approved