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%I #4 May 07 2018 08:56:14
%S 0,1,1,1,7,1,2,14,14,2,3,33,18,33,3,5,70,25,25,70,5,8,157,113,61,113,
%T 157,8,13,346,238,157,157,238,346,13,21,769,359,117,1198,117,359,769,
%U 21,34,1710,1309,244,3484,3484,244,1309,1710,34,55,3813,3091,936,5336,13152
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1....1...2.....3......5......8.......13........21........34.........55
%C ..1....7...14..33....70....157....346......769......1710......3813.......8514
%C ..1...14...18..25...113....238....359.....1309......3091......5173......15475
%C ..2...33...25..61...157....117....244......936.......733......1513.......5788
%C ..3...70..113.157..1198...3484...5336....24401.....90422....181207.....546435
%C ..5..157..238.117..3484..13152..12582...139840....774023...1302357....5969791
%C ..8..346..359.244..5336..12582...6492...218516....748819....579549....8291908
%C .13..769.1309.936.24401.139840.218516..1429403..12033436..34502082..116115677
%C .21.1710.3091.733.90422.774023.748819.12033436.180869894.471888374.2046852451
%H R. H. Hardin, <a href="/A304149/b304149.txt">Table of n, a(n) for n = 1..264</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 17] for n>22
%F k=5: [order 93] for n>96
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..0
%e ..1..0..1..1. .1..1..0..1. .1..0..0..1. .1..1..0..0. .1..0..1..1
%e ..1..1..0..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e ..1..0..1..1. .0..1..1..1. .0..1..1..1. .1..0..1..1. .1..0..0..1
%e ..0..1..1..0. .0..0..1..0. .0..0..1..0. .0..0..1..0. .0..1..1..0
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 07 2018
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