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%I #4 Jul 27 2018 22:12:26
%S 0,1,1,1,7,1,2,16,16,2,3,45,61,45,3,5,120,201,201,120,5,8,333,863,
%T 1140,863,333,8,13,928,3666,6964,6964,3666,928,13,21,2613,14831,39216,
%U 67214,39216,14831,2613,21,34,7400,61638,225065,594763,594763,225065,61638
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1......1.......2.........3...........5.............8.............13
%C ..1....7.....16......45.......120.........333...........928...........2613
%C ..1...16.....61.....201.......863........3666.........14831..........61638
%C ..2...45....201....1140......6964.......39216........225065........1322225
%C ..3..120....863....6964.....67214......594763.......5282805.......47791350
%C ..5..333...3666...39216....594763.....8362442.....113897676.....1604462254
%C ..8..928..14831..225065...5282805...113897676....2326497716....49910970516
%C .13.2613..61638.1322225..47791350..1604462254...49910970516..1648608723762
%C .21.7400.255772.7638732.429692708.22617426590.1074044399955.54927936213579
%H R. H. Hardin, <a href="/A317436/b317436.txt">Table of n, a(n) for n = 1..180</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) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 20] for n>21
%F k=4: [order 68] for n>70
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..0
%e ..1..0..0..1. .0..1..1..1. .1..0..1..1. .1..1..0..1. .1..1..1..0
%e ..0..0..0..0. .1..0..1..0. .0..1..0..1. .1..1..1..1. .0..0..0..1
%e ..0..0..1..1. .1..1..1..1. .0..0..0..1. .0..1..1..0. .0..1..1..0
%e ..1..0..0..1. .0..1..1..0. .0..1..0..1. .1..1..1..1. .0..0..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304013.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 27 2018
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