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Results tagged with trees
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user 1907
A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
7
votes
1
answer
455
views
More asymptotics for trees
Consider rooted trees where all vertices at the same level have the same number of children and this is $\geq 3$ except for leaves. … If we let $s(n)$ denote the number of such trees with $n$ nodes then we get a sequence for $n \geq 1$:
1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... …
- 1,305
3
votes
More asymptotics for trees
I'd like to promote Lucia's comment to an answer if I could but apparently I can't. I'll just fill in a few of the details. The basic idea is to pretend that $S(x) = C x^{\alpha}$. Plug in to the recu …
- 1,305
14
votes
1
answer
696
views
Are the asymptotics of A003238 known?
Sequence A003238 of the OEIS counts ``rooted trees with $n$ vertices in which vertices at the same level have the same degree.'' The sequence, $a$, begins
1, 1, 2, 3, 5, 6, 10, 11, 16, ... …
- 1,305