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%I #4 May 16 2018 14:47:36
%S 1,1,1,1,4,1,1,7,7,1,1,13,13,13,1,1,26,23,23,26,1,1,49,45,56,45,49,1,
%T 1,99,131,199,199,131,99,1,1,194,337,598,897,598,337,194,1,1,387,883,
%U 1950,3525,3525,1950,883,387,1,1,773,2389,6588,15544,20932,15544,6588,2389
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1....1.....1......1.......1........1.........1...........1............1
%C .1...4....7....13.....26......49.......99.......194.........387..........773
%C .1...7...13....23.....45.....131......337.......883........2389.........6599
%C .1..13...23....56....199.....598.....1950......6588.......21871........72947
%C .1..26...45...199....897....3525....15544.....68896......310438......1387613
%C .1..49..131...598...3525...20932...122388....711362.....4369285.....26155072
%C .1..99..337..1950..15544..122388...930123...7208807....57718628....454436233
%C .1.194..883..6588..68896..711362..7208807..73484449...779364745...8098139458
%C .1.387.2389.21871.310438.4369285.57718628.779364745.11082127004.153249721883
%H R. H. Hardin, <a href="/A304676/b304676.txt">Table of n, a(n) for n = 1..197</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F k=3: [order 18] for n>19
%F k=4: [order 70] for n>71
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..0
%e ..1..1..0..1. .0..0..0..0. .0..0..0..0. .0..1..0..1. .1..1..0..1
%e ..0..1..0..1. .0..0..0..0. .1..1..1..1. .0..0..0..1. .0..1..0..1
%e ..0..0..1..1. .0..0..0..0. .1..1..1..1. .1..1..0..1. .0..0..1..1
%e ..1..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..0. .1..1..1..0
%Y Column 2 is A304004.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 16 2018
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