%I #4 May 11 2016 15:21:42
%S 1,1,1,1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,3,0,0,3,
%T 0,1,1,0,0,0,0,0,0,0,1,1,0,2,0,0,0,0,2,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,
%U 2,0,4,0,0,4,0,2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,0,2,0,0,0,0,2,0,2,0,1,1,0,0
%N 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.
%C Table starts
%C .1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1
%C .1.0.1.0.0.0.0.0.0.0.0.0.0.0.0.0
%C .1.1.0.0.0.3.0.2.0.2.0.2.0.2.0
%C .1.0.0.0.0.0.0.0.0.0.0.0.0.0
%C .1.0.0.0.0.0.0.4.0.2.0.0.0
%C .1.0.3.0.0.0.0.0.0.0.1.8
%C .1.0.0.0.0.0.0.0.0.3.0
%C .1.0.2.0.4.0.0.0.1
%C .1.0.0.0.0.0.0.1
%C .1.0.2.0.2.0.3
%C .1.0.0.0.0.1
%C .1.0.2.0.0
%C .1.0.0.0
%C .1.0.2
%C .1.0
%C .1
%H R. H. Hardin, <a href="/A272974/b272974.txt">Table of n, a(n) for n = 1..143</a>
%F Row n extended:
%F n=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 0
%F n=3: 1 1 0 0 0 3 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2
%F n=4: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%F n=5: 1 0 0 0 0 0 0 4 0 2 0 0 0 0 0
%F n=6: 1 0 3 0 0 0 0 0 0 0 1 8 0
%e All solutions for n=3 k=6
%e ..0..1..1..1..1..0. .1..0..0..0..0..1. .1..1..0..0..1..1
%e ..1..0..0..0..0..1. .1..0..0..0..0..1. .0..0..0..0..0..0
%e ..1..0..0..0..0..1. .0..1..1..1..1..0. .1..1..0..0..1..1
%K nonn,tabl
%O 1,31
%A _R. H. Hardin_, May 11 2016