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%I #4 May 25 2018 08:20:37
%S 0,1,1,1,7,1,2,14,14,2,3,33,22,33,3,5,70,34,34,70,5,8,157,182,91,182,
%T 157,8,13,346,438,352,352,438,346,13,21,769,920,372,3384,372,920,769,
%U 21,34,1710,3431,1016,15814,15814,1016,3431,1710,34,55,3813,9510,3474,39016
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 6 or 7 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...14...33......70......157.......346........769.........1710
%C ..1...14...22...34.....182......438.......920.......3431.........9510
%C ..2...33...34...91.....352......372......1016.......3474.........4945
%C ..3...70..182..352....3384....15814.....39016.....211725......1172982
%C ..5..157..438..372...15814...101803....285422....3531950.....30133609
%C ..8..346..920.1016...39016...285422....630306...12378708....108542087
%C .13..769.3431.3474..211725..3531950..12378708..219093711...4455522372
%C .21.1710.9510.4945.1172982.30133609.108542087.4455522372.154688671720
%H R. H. Hardin, <a href="/A305089/b305089.txt">Table of n, a(n) for n = 1..220</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) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 14] for n>16
%F k=4: [order 19] for n>24
%F k=5: [order 97] for n>101
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..1
%e ..1..1..0..1. .1..1..1..1. .0..1..0..0. .1..0..1..1. .1..1..0..0
%e ..1..1..1..1. .1..1..0..1. .0..0..0..0. .1..1..1..1. .1..1..1..0
%e ..0..0..1..1. .1..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..1..1
%e ..1..0..1..0. .0..1..1..0. .1..1..0..0. .0..1..0..0. .0..0..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304143.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 25 2018
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