%I #4 Nov 21 2016 09:11:52

%S 0,0,0,1,20,1,15,264,264,15,90,2550,9354,2550,90,357,22267,201539,

%T 201539,22267,357,1107,166762,3576730,11454780,3576730,166762,1107,

%U 2907,1046418,58069125,514122657,514122657,58069125,1046418,2907,6765,5586207

%N T(n,k)=Number of nXk 0..2 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

%C Table starts

%C .....0.........0.............1................15....................90

%C .....0........20...........264..............2550.................22267

%C .....1.......264..........9354............201539...............3576730

%C ....15......2550........201539..........11454780.............514122657

%C ....90.....22267.......3576730.........514122657...........62922179364

%C ...357....166762......58069125.......20086951472.........6584300364020

%C ..1107...1046418.....859516239......724313811311.......615691843257769

%C ..2907...5586207...11336482734....24378309172117.....53477639726024161

%C ..6765..25997719..132278417831...757386980723842...4387410446730955493

%C .14355.107862842.1373129978107.21490393664858691.339567886171232998387

%H R. H. Hardin, <a href="/A278414/b278414.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

%F k=1: [polynomial of degree 8]

%F k=2: [polynomial of degree 26]

%F k=3: [polynomial of degree 80]

%e Some solutions for n=3 k=4

%e ..1..0..1..2. .0..0..0..0. .0..1..2..0. .0..1..1..2. .1..2..1..2

%e ..0..0..0..2. .1..1..0..1. .0..0..0..1. .0..1..0..2. .0..2..1..0

%e ..2..2..2..1. .0..2..1..1. .2..2..0..1. .2..0..0..2. .0..2..1..1

%Y Column 1 is A005716(n+1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 21 2016