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

Bob Selcoe rselcoe at entouchonline.net
Mon Apr 25 23:38:32 CEST 2016


Nice solution, Rob!

Is the general idea worth exploring for a new sequence?  It seems 
sufficiently different from A219760.

Cheers,
Bob

--------------------------------------------------
From: "Rob Pratt" <Rob.Pratt at sas.com>
Sent: Monday, April 25, 2016 4:18 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Minimum number of points on an n X k grid forcingtheformationof isoceles triangles

> 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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