OFFSET
1,4
COMMENTS
Colijn and Plazzotta enumerate rooted binary trees (every vertex 0 or 2 children) by n=1 as a singleton and thereafter tree n is a root with child subtrees x = A002024(n-1) and y = A002260(n-1).
Each row starts with 1's for the childless vertices (A064064(n) of them).
Each row ends with n itself (the tree root).
The second last term in each row is the numerically largest subtree of the root, which is x.
Row lengths are A064002(n), the number of vertices.
LINKS
Kevin Ryde, Table of n, a(n) for rows 1..500, flattened
Caroline Colijn and Giacomo Plazzotta, A Metric on Phylogenetic Tree Shapes, Systematic Biology, volume 67, number 1, January 2018, pages 113-126, see section 2.3 where their L_n = row n here.
Kevin Ryde, PARI/GP Code
EXAMPLE
Triangle begins:
k=1 2 3 4 5 6 7 8 9 10 11
n=1: 1,
n=2: 1, 1, 2,
n=3: 1, 1, 1, 2, 3,
n=4: 1, 1, 1, 1, 2, 2, 4,
n=5: 1, 1, 1, 1, 2, 3, 5,
n=6: 1, 1, 1, 1, 1, 2, 2, 3, 6,
n=7: 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 7,
n=8: 1, 1, 1, 1, 1, 2, 2, 4, 8,
Tree n=6 and its subtree numbers are as follows and row 6 is these subtree numbers in ascending order.
6 root
/ \
3 2
/ \ / \
2 1 1 1
/ \
1 1
PROG
(PARI) See links.
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Kevin Ryde, Sep 19 2022
STATUS
approved