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%I #4 Jul 09 2018 11:29:15
%S 0,1,1,1,3,1,2,11,11,2,3,10,15,10,3,5,51,33,33,51,5,8,165,117,42,117,
%T 165,8,13,306,247,277,277,247,306,13,21,993,599,954,3988,954,599,993,
%U 21,34,2867,1757,2432,13869,13869,2432,1757,2867,34,55,6818,4241,10541,54941
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 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....3...11....10......51.....165.......306........993........2867
%C ..1...11...15....33.....117.....247.......599.......1757........4241
%C ..2...10...33....42.....277.....954......2432......10541.......39013
%C ..3...51..117...277....3988...13869.....54941.....427096.....1946889
%C ..5..165..247...954...13869...43604....228056....1976020.....9093873
%C ..8..306..599..2432...54941..228056...1396674...17049299...106043303
%C .13..993.1757.10541..427096.1976020..17049299..331807728..2594184863
%C .21.2867.4241.39013.1946889.9093873.106043303.2594184863.22368384180
%H R. H. Hardin, <a href="/A316648/b316648.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
%F k=3: [order 17]
%F k=4: [order 69] for n>70
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..0
%e ..0..1..1..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .1..0..0..1
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .1..1..0..0. .0..0..0..0
%e ..1..0..1..0. .0..1..1..0. .1..0..0..1. .0..1..0..1. .0..0..0..0
%e ..0..0..0..0. .0..1..1..0. .1..0..0..1. .0..1..0..1. .0..1..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304052.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 09 2018
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