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%I #4 May 04 2018 11:32:24
%S 0,1,1,1,7,1,2,16,16,2,3,45,38,45,3,5,120,103,103,120,5,8,333,281,370,
%T 281,333,8,13,928,826,1318,1318,826,928,13,21,2613,2421,4449,5162,
%U 4449,2421,2613,21,34,7400,7104,16187,20979,20979,16187,7104,7400,34,55,21053
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 5 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....38....103.....281......826.....2421......7104......20732
%C ..2...45...103....370....1318.....4449....16187.....57097.....204138
%C ..3..120...281...1318....5162....20979....87747....363807....1503951
%C ..5..333...826...4449...20979....99733...488944...2363993...11464178
%C ..8..928..2421..16187...87747...488944..2820436..16004647...90893514
%C .13.2613..7104..57097..363807..2363993.16004647.106817959..709737869
%C .21.7400.20732.204138.1503951.11464178.90893514.709737869.5516875986
%H R. H. Hardin, <a href="/A304019/b304019.txt">Table of n, a(n) for n = 1..219</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 20]
%F k=4: [order 66] for n>67
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..0
%e ..1..0..0..0. .0..0..1..1. .1..1..1..1. .0..1..0..1. .1..0..0..1
%e ..0..0..0..1. .0..1..1..0. .1..1..1..1. .1..1..1..0. .0..0..0..0
%e ..0..0..0..0. .1..0..0..0. .0..1..1..0. .0..1..1..0. .1..0..0..1
%e ..1..0..1..0. .0..1..1..1. .0..0..1..1. .1..1..1..0. .0..0..1..1
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 04 2018
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