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%I #4 Jul 26 2018 16:52:58
%S 0,1,1,1,7,1,2,23,23,2,3,86,91,86,3,5,313,529,529,313,5,8,1145,2870,
%T 4811,2870,1145,8,13,4184,15382,42512,42512,15382,4184,13,21,15293,
%U 83982,360940,659721,360940,83982,15293,21,34,55895,455180,3113246,9218534
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1.......1.........2...........3.............5...............8
%C ..1.....7......23........86.........313..........1145............4184
%C ..1....23......91.......529........2870.........15382...........83982
%C ..2....86.....529......4811.......42512........360940.........3113246
%C ..3...313....2870.....42512......659721.......9218534.......134524463
%C ..5..1145...15382....360940.....9218534.....205048072......4822465183
%C ..8..4184...83982...3113246...134524463....4822465183....185409601420
%C .13.15293..455180..26916032..1959207396..113269475813...7139196864817
%C .21.55895.2470224.231704568.28331771091.2632551285887.270802813530242
%H R. H. Hardin, <a href="/A317376/b317376.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F k=3: [order 15] for n>16
%F k=4: [order 50] for n>51
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..0..0..1. .0..0..1..1
%e ..0..1..0..1. .0..0..0..1. .1..0..0..0. .1..0..1..1. .1..1..0..1
%e ..1..0..0..1. .0..1..1..1. .0..1..1..1. .0..1..1..1. .1..1..1..1
%e ..0..0..0..0. .1..1..1..1. .0..1..1..1. .1..0..0..0. .0..1..0..1
%e ..1..1..1..1. .0..1..0..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A303890.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 26 2018
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