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%I #4 Jun 01 2018 11:04:45
%S 0,1,1,1,3,1,2,11,11,2,3,10,7,10,3,5,51,20,20,51,5,8,165,44,26,44,165,
%T 8,13,306,77,169,169,77,306,13,21,993,181,475,1275,475,181,993,21,34,
%U 2867,379,1234,2697,2697,1234,379,2867,34,55,6818,849,5007,13128,5443,13128
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1...1.....2......3......5.......8.......13........21.........34
%C ..1....3..11....10.....51....165.....306......993......2867.......6818
%C ..1...11...7....20.....44.....77.....181......379.......849.......1799
%C ..2...10..20....26....169....475....1234.....5007.....16422......51196
%C ..3...51..44...169...1275...2697...13128....58608....222877.....971263
%C ..5..165..77...475...2697...5443...30344...132479....485885....2234246
%C ..8..306.181..1234..13128..30344..222961..1378090...6504099...42968149
%C .13..993.379..5007..58608.132479.1378090.10709608..62295992..516604339
%C .21.2867.849.16422.222877.485885.6504099.62295992.362139243.3817890104
%H R. H. Hardin, <a href="/A305452/b305452.txt">Table of n, a(n) for n = 1..220</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) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
%F k=3: [order 17] for n>18
%F k=4: [order 63] for n>65
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0
%e ..1..1..1..0. .1..0..0..0. .1..0..0..1. .1..1..1..0. .0..0..0..0
%e ..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e ..0..1..1..0. .1..0..0..1. .0..0..0..1. .0..0..1..1. .1..0..0..1
%e ..0..1..1..0. .0..0..1..0. .0..1..0..0. .0..1..0..1. .0..1..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304052.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 01 2018
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