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%I #4 Jun 15 2018 06:20:05
%S 0,1,1,1,7,1,2,25,25,2,3,98,132,98,3,5,383,919,919,383,5,8,1493,6030,
%T 11142,6030,1493,8,13,5824,39985,129452,129452,39985,5824,13,21,22717,
%U 264680,1510278,2617757,1510278,264680,22717,21,34,88609,1752681
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1........1..........2............3..............5.................8
%C ..1.....7.......25.........98..........383...........1493..............5824
%C ..1....25......132........919.........6030..........39985............264680
%C ..2....98......919......11142.......129452........1510278..........17617201
%C ..3...383.....6030.....129452......2617757.......53422574........1088558635
%C ..5..1493....39985....1510278.....53422574.....1909062568.......68109190612
%C ..8..5824...264680...17617201...1088558635....68109190612.....4251930563544
%C .13.22717..1752681..205511593..22189910134..2430866826404...265585355341963
%C .21.88609.11604776.2397335154.452276452312.86749580967244.16586555684575766
%H R. H. Hardin, <a href="/A305961/b305961.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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
%F k=3: [order 9] for n>10
%F k=4: [order 28] for n>29
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..0..1. .0..1..0..0. .0..1..1..0. .0..0..1..1
%e ..1..1..1..0. .0..1..1..1. .0..0..1..1. .0..0..1..1. .1..0..0..0
%e ..1..1..1..1. .1..1..0..0. .0..1..1..1. .1..0..0..0. .0..0..0..1
%e ..0..1..1..0. .1..0..0..0. .1..0..1..0. .1..0..0..1. .1..0..0..0
%e ..1..1..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..1. .1..0..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304421.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 15 2018
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