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A274065 T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..2 order.

%I A274065 #4 Jun 09 2016 07:54:52
%S A274065 1,2,2,5,9,5,14,50,50,14,41,285,264,285,41,122,1617,435,435,1617,122,
%T A274065 365,9188,546,8,546,9188,365,1094,52193,1209,1,1,1209,52193,1094,3281,
%U A274065 296511,3272,0,0,0,3272,296511,3281,9842,1684466,8412,0,0,0,0,8412,1684466,9842
%N A274065 T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..2 order.
%C A274065 Table starts
%C A274065 .....1.......2.....5..14...41..122...365...1094....3281....9842.29525
%C A274065 .....2.......9....50.285.1617.9188.52193.296511.1684466.9569425
%C A274065 .....5......50...264.435..546.1209..3272...8412...20634
%C A274065 ....14.....285...435...8....1....0.....0......0
%C A274065 ....41....1617...546...1....0....0.....0
%C A274065 ...122....9188..1209...0....0....0
%C A274065 ...365...52193..3272...0....0
%C A274065 ..1094..296511..8412...0
%C A274065 ..3281.1684466.20634
%C A274065 ..9842.9569425
%C A274065 .29525
%H A274065 R. H. Hardin, <a href="/A274065/b274065.txt">Table of n, a(n) for n = 1..66</a>
%F A274065 Empirical for column k:
%F A274065 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A274065 k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
%F A274065 k=3: [order 40] for n>49
%e A274065 Some solutions for n=4 k=4
%e A274065 ..0..1..0..2. .0..1..2..1. .0..0..0..1. .0..1..1..2. .0..0..1..1
%e A274065 ..2..2..2..0. .1..0..0..0. .2..2..2..1. .1..0..2..1. .2..1..0..2
%e A274065 ..1..1..1..0. .1..2..2..2. .1..1..1..2. .2..0..2..0. .2..1..0..2
%e A274065 ..0..2..0..1. .2..1..0..1. .0..0..0..2. .1..0..2..1. .2..1..0..2
%Y A274065 Column 1 is A007051(n-1).
%Y A274065 Column 2 is A231413(n-1).
%K A274065 nonn,tabl
%O A274065 1,2
%A A274065 _R. H. Hardin_, Jun 09 2016