OFFSET
1,2
COMMENTS
The top-down definition of the binomial tree suits Matula-Goebel numbering: The tree of n = 2^k + r vertices, for 1 <= r <= 2^k is the binomial tree of 2^k vertices and a child subtree under the root which is the binomial tree of r vertices.
In the tree of n vertices, adding a new singleton child under each vertex gives the tree of 2*n vertices, so that a(2*n) = A348067(a(n)).
LINKS
Kevin Ryde, Table of n, a(n) for n = 1..117
Kevin Ryde, PARI/GP Code
FORMULA
a(2^k + r) = a(2^k) * prime(a(r)) for 1 <= r <= 2^k.
a(2^k) = A076146(k+1), being a tree of order k.
EXAMPLE
The tree of n=13 vertices numbered 0..12 is
0
| \ \ \
1 2 4 8
| | \ | \ \
3 5 6 9 10 12
| |
7 11
Vertices 0..7 are the binomial tree of 2^k = 8 vertices, and vertices 8..12 are the binomial tree of 5 vertices.
Using the recurrence, a(13) = a(8 + 5) = a(8) * prime(a(5)) = 78*37 = 2886.
PROG
(PARI) \\ See links.
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Kevin Ryde, Nov 25 2022
STATUS
approved