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

[Chris]

Also, for k = 2, a(n) = a(n-1) + a(n-2) + (n+1)(3-(-1)^(n+1))/4

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Ron Hardin
Sent: Sunday, April 24, 2016 23:42
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: No isosceles triangles in a square grid, continued

T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no three 1s forming an isosceles right triangle


..1....2.....3......4......5......6......7......8......9
..2....6....10.....21.....34.....62....100....171....276
..3...10....24.....24....107....236....499...1228...2753
..4...21....24.....60....210....637...1840...5792..18556
..5...34...107....210....768...1898...8211..37402.192579
..6...62...236....637...1898...7468..26052.138476.831738
..7..100...499...1840...8211..26052.131056.648178.......
..8..171..1228...5792..37402.138476.648178..............
..9..276..2753..18556.192579.831738.....................
.10..458..6292..54034.635086............................
.11..740.14751.160246...................................
.12.1211.34824..........................................
.13.1958................................................
.14.....................................................
So far only cols 1 and 2 have recurrences Empirical for column k:
k=1: a(n)=2*a(n-1)-a(n-2)
k=2: a(n)=a(n-1)+3*a(n-2)-2*a(n-3)-3*a(n-4)+a(n-5)+a(n-6)
Column 3 does not look promising for a recurrence, after 94 terms.
work not double-checked! rhhardin at mindspring.com rhhardin at att.net (either)

 
  

   

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