# [seqfan] Re: No isosceles triangles in a square grid, continued

Ron Hardin rhhardin at att.net
Wed Apr 27 22:40:00 CEST 2016

```After a few hours with n+k-1 (after which progress will slow or stop):

T(n,k)=Number of nXk 0..1 arrays with exactly n+k-1 having value 1 and no three 1s forming an isosceles triangle
Table starts
.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1
.1.0.1.0.0.0.0.0.0.0.0.0.0.0.0.0..
.1.1.0.0.0.3.0.2.0.2.0.2.0.2.0....
.1.0.0.0.0.0.0.0.0.0.0.0.0.0......
.1.0.0.0.0.0.0.4.0.2.0.0.0........
.1.0.3.0.0.0.0.0.0.0.1.8..........
.1.0.0.0.0.0.0.0.0.3..............
.1.0.2.0.4.0.0.0.1................
.1.0.0.0.0.0.0.1..................
.1.0.2.0.2.0.3....................
.1.0.0.0.0.1......................
.1.0.2.0.0........................
.1.0.0.0..........................
.1.0.2............................
.1.0..............................
.1................................
column 2: 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
column 3: 1 1 0 0 0 3 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0
column 4: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
column 5: 1 0 0 0 0 0 0 4 0 2 0 0 0
--
rhhardin at mindspring.com rhhardin at att.net (either)

From: Ron Hardin <rhhardin at att.net>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Wednesday, April 27, 2016 12:03 PM
Subject: [seqfan] Re: No isosceles triangles in a square grid, continued

Simple to do, yes.  I can't reach far into the diagonal however owing to a memory blowup, which stops the antidiagonal search (which is the reason for doing columns independently of antidiagonal search).
rhhardin at mindspring.com rhhardin at att.net (either)

From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Wednesday, April 27, 2016 11:48 AM
Subject: [seqfan] Re: No isosceles triangles in a square grid, continued

Ron, would it be a simple matter to run
Tminusone(n,k)=Number of nXk 0..1 arrays with exactly n+k-1 having value 1
and no three 1s forming an isosceles triangle
(where I have replaced n+k-2 with n+k-1) ?

```