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%I #4 Jul 06 2018 12:35:20
%S 1,2,2,3,5,3,5,7,7,5,8,17,10,17,8,13,35,17,17,35,13,21,61,36,42,36,61,
%T 21,34,127,69,89,89,69,127,34,55,265,129,187,251,187,129,265,55,89,
%U 507,260,430,621,621,430,260,507,89,144,1013,544,1046,1568,1811,1568,1046,544
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 7 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
%C ..2...5...7...17....35....61....127.....265.....507.....1013......2071
%C ..3...7..10...17....36....69....129.....260.....544.....1125......2348
%C ..5..17..17...42....89...187....430....1046....2407.....5706.....13873
%C ..8..35..36...89...251...621...1568....4269...11869....33451.....95326
%C .13..61..69..187...621..1811...5265...17004...54443...174625....570128
%C .21.127.129..430..1568..5265..18978...73409..276005..1055277...4099795
%C .34.265.260.1046..4269.17004..73409..336604.1492856..6793881..31252764
%C .55.507.544.2407.11869.54443.276005.1492856.7870292.42144065.228096346
%H R. H. Hardin, <a href="/A316552/b316552.txt">Table of n, a(n) for n = 1..263</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) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 15]
%F k=4: [order 45] for n>48
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..1..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0
%e ..0..1..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e ..0..0..0..0. .1..1..1..1. .1..1..0..0. .0..1..0..0. .0..0..0..0
%e ..1..1..1..0. .1..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
%e ..0..1..1..1. .1..1..0..0. .0..1..1..0. .0..0..0..0. .0..0..1..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A303802.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 06 2018
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