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%I #4 Jan 25 2018 08:37:20
%S 0,1,1,0,4,0,1,3,3,1,0,13,0,13,0,1,32,2,2,32,1,0,53,6,11,6,53,0,1,125,
%T 20,32,32,20,125,1,0,386,22,87,781,87,22,386,0,1,727,92,110,1354,1354,
%U 110,92,727,1,0,1601,206,385,2409,3950,2409,385,206,1601,0,1,4568,460,908
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0...1...0...1......0......1.......0........1.........0..........1...........0
%C .1...4...3..13.....32.....53.....125......386.......727.......1601........4568
%C .0...3...0...2......6.....20......22.......92.......206........460........1176
%C .1..13...2..11.....32.....87.....110......385.......908.......2760........6454
%C .0..32...6..32....781...1354....2409....34250....109459.....294045.....2120905
%C .1..53..20..87...1354...3950....9586....92375....384519....1468344.....9531019
%C .0.125..22.110...2409...9586...17377...241249...1201122....6055242....45702804
%C .1.386..92.385..34250..92375..241249..8695221..49691754..274634548..4587455345
%C .0.727.206.908.109459.384519.1201122.49691754.359275256.2514115870.49068141912
%H R. H. Hardin, <a href="/A298712/b298712.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-2)
%F k=2: a(n) = a(n-1) +a(n-2) +8*a(n-3) -16*a(n-5)
%F k=3: [order 17] for n>18
%F k=4: [order 70]
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..1..1. .0..1..1..1
%e ..0..1..0..1. .0..0..1..0. .0..0..0..0. .1..0..1..1. .1..0..1..1
%e ..1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
%e ..0..1..0..1. .0..0..1..0. .0..0..1..1. .1..0..1..1. .0..1..1..1
%e ..0..1..0..1. .0..0..0..1. .0..0..0..0. .1..0..1..1. .1..0..1..1
%Y Column 2 is A298057.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 25 2018
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