%I #4 Jul 09 2018 11:20:03
%S 0,1,1,1,7,1,2,16,16,2,3,45,43,45,3,5,120,122,122,120,5,8,333,404,524,
%T 404,333,8,13,928,1344,2342,2342,1344,928,13,21,2613,4583,9773,14568,
%U 9773,4583,2613,21,34,7400,15737,44095,85222,85222,44095,15737,7400,34
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1.....1......2........3.........5..........8...........13............21
%C ..1....7....16.....45......120.......333........928.........2613..........7400
%C ..1...16....43....122......404......1344.......4583........15737.........53378
%C ..2...45...122....524.....2342......9773......44095.......195387........864584
%C ..3..120...404...2342....14568.....85222.....532401......3294736......20347911
%C ..5..333..1344...9773....85222....684269....5879970.....50360206.....428319949
%C ..8..928..4583..44095...532401...5879970...69857903....835457349....9913271027
%C .13.2613.15737.195387..3294736..50360206..835457349..14106315869..235116618481
%C .21.7400.53378.864584.20347911.428319949.9913271027.235116618481.5489873419154
%H R. H. Hardin, <a href="/A316641/b316641.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) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 19] for n>21
%F k=4: [order 69] for n>71
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..0..0..0
%e ..1..0..1..1. .0..1..1..0. .1..1..1..1. .1..0..0..1. .1..1..1..0
%e ..0..0..0..1. .1..0..1..1. .0..1..1..0. .0..0..0..0. .1..1..1..0
%e ..1..0..0..0. .1..1..1..1. .0..0..1..1. .0..0..0..1. .1..0..0..0
%e ..0..0..0..1. .0..1..1..0. .0..1..1..0. .1..0..1..1. .0..0..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304013.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 09 2018