2
votes
1answer
167 views

More asymptotics for trees

This is a follow up to my recent question on the asymptotics of A003238. Lucia gave a fine answer to that question, but as I hinted the 'real' problem I have in mind is slightly different, and I've ...
13
votes
1answer
374 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, ... and it is ...
3
votes
1answer
219 views

Flow of an integer

I've stumbled across this family of flow networks, and posted the sequence of maximal flows to OEIS. It doesn't appear at this time. I can't find any reference to it either. Has anyone seen it? ...
3
votes
2answers
134 views

Databases for sequences indexed by partitions

Is there a database for sequences indexed by partitions similar to Sloane's OEIS? I mean, I am aware that in the OEIS there are some arrays indexed by partitions, but I feel as though most of such ...
4
votes
0answers
309 views

Number of Configurations in the optimal Hanoi tower

There is a unique strategy how to move $n$ disks from the first rod to the second optimally and it takes $2^n-1$ steps, solution is obtained by simple recursion. I am interested into the following ...
1
vote
1answer
273 views

Maximal difference between k randomly drawn numbers from 1 to n – Looking for formula to sequence

Hello! I have an interesting problem that seemed simple to me, but I'm unable to solve it on my own. Suppose I am drawing k numbers out of n numbers labeled from 1 to n. Considering all ...
6
votes
2answers
499 views

Maximal number of edges and triangular cells for n points in a triangular lattice

Consider a subset of $n$ points in an equilateral triangular lattice. Draw all the edges between nearest-neighbor points. What is the maximum, over all such subsets, of the number of edges? This ...
18
votes
3answers
1k views

Zeroes of the random Fibonacci sequence

Let X_n be the "random Fibonacci sequence," defined as follows: $X_0 = 0, X_1 = 1$; $X_n = \pm X_{n-1} \pm X_{n-2}$, where the signs are chosen by independent 50/50 coinflips. It is known that ...
7
votes
4answers
768 views

A Pascal's-triangle -like random process

I was exploring Pascal's triangle on a cylinder when I encountered this puzzle-like problem. It is surely elementary, but perhaps weekend-entertaining. Start with a permutation of $(1,2,3, \ldots, ...
10
votes
1answer
525 views

Put as many points as possible in an equilateral triangle of side 1 with their minimal distance greater than 1/n

It is known by the pigeon-hole principle that: If we select $5$ points within an equilateral triangle with side $1$, there must be at least two whose distance apart is less than or equal to $1/2$. ...