[seqfan] Re: Minimum number of points on an n X k grid forcing the formation of isoceles triangles

[Rob Pratt]

6 is optimal:

X O X O X O O X O
O O O O X O X O O
O O O O O O O O O

Your variant is similar to this one:
https://oeis.org/A219760

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob Selcoe
Sent: Monday, April 25, 2016 3:37 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Minimum number of points on an n X k grid forcing the formation of isoceles triangles

Hi Seqfans,

A271914 shows the array for maximum number of points that can be chosen in an n X k grid such that no three distinct points form an isosceles triangle.

But what about the minimum number T(n,k) that can be chosen so that no three distinct points form an isosceles triangle, but any additional point will form of one?  We can safely say T(n,1) = n; but beyond that it gets more interesting and might make a nice companion entry tor A271914.

So for example, T(9,1) = 9, but T(9,3) <= 7:

o o X o o X X X X
o o X o o o o o o
o o X o o o o o o

There are many other configurations with 7 points.  Any < 7?

Cheers,
Bob Selcoe








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