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%I #4 Jun 02 2018 08:54:55
%S 1,2,2,3,5,3,5,7,7,5,8,17,10,17,8,13,31,21,21,31,13,21,49,40,48,40,49,
%T 21,34,103,70,98,98,70,103,34,55,193,125,192,277,192,125,193,55,89,
%U 327,231,368,577,577,368,231,327,89,144,641,419,732,1245,1558,1245,732,419,641
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1...2...3....5....8....13.....21.....34......55......89......144.......233
%C ..2...5...7...17...31....49....103....193.....327.....641.....1207......2129
%C ..3...7..10...21...40....70....125....231.....419.....752.....1365......2482
%C ..5..17..21...48...98...192....368....732....1480....2932.....5776.....11486
%C ..8..31..40...98..277...577...1245...2868....6381...14206....31630.....70391
%C .13..49..70..192..577..1558...3910..10465...27679...70960...185085....482009
%C .21.103.125..368.1245..3910..11438..34687..106558..317866...952180...2866802
%C .34.193.231..732.2868.10465..34687.123104..440388.1501195..5216253..18221847
%C .55.327.419.1480.6381.27679.106558.440388.1894686.7620015.31132355.129187191
%H R. H. Hardin, <a href="/A305482/b305482.txt">Table of n, a(n) for n = 1..420</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) +4*a(n-3) -2*a(n-4) for n>5
%F k=3: a(n) = a(n-1) +3*a(n-3) -2*a(n-6) for n>9
%F k=4: [order 10] for n>13
%F k=5: [order 29] for n>33
%F k=6: [order 60] for n>66
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..0..0..1. .0..0..0..0
%e ..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .1..0..0..0
%e ..0..0..1..0. .0..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0
%e ..1..0..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .0..0..0..0
%e ..1..1..1..1. .1..0..0..0. .0..0..1..1. .1..1..0..1. .1..0..0..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A303677.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 02 2018
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