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%I #4 Jul 12 2018 11:53:02
%S 0,0,0,0,3,0,0,5,5,0,0,18,4,18,0,0,61,46,46,61,0,0,209,151,410,151,
%T 209,0,0,702,543,2397,2397,543,702,0,0,2381,2120,13970,26845,13970,
%U 2120,2381,0,0,8069,8155,93426,219766,219766,93426,8155,8069,0,0,27330,30205,586718
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0....0.....0.......0.........0..........0............0..............0
%C .0....3.....5......18........61........209..........702...........2381
%C .0....5.....4......46.......151........543.........2120...........8155
%C .0...18....46.....410......2397......13970........93426.........586718
%C .0...61...151....2397.....26845.....219766......2442827.......24591846
%C .0..209...543...13970....219766....2605126.....42857655......625815905
%C .0..702..2120...93426...2442827...42857655...1169271436....26888275330
%C .0.2381..8155..586718..24591846..625815905..26888275330...947123604065
%C .0.8069.30205.3677924.242436003.9056077433.613862574233.33009635701375
%H R. H. Hardin, <a href="/A316763/b316763.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 18]
%F k=4: [order 66] for n>67
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
%e ..1..1..0..0. .0..1..0..1. .1..0..0..1. .1..1..1..1. .1..0..0..0
%e ..0..0..0..1. .0..0..0..0. .0..0..1..0. .1..1..0..0. .1..0..1..0
%e ..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..0. .0..0..1..1
%e ..1..1..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..1..0
%Y Column 2 is A303684.
%Y Column 3 is A305170.
%Y Column 4 is A305171.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 12 2018
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