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%I #4 Apr 06 2018 12:42:28
%S 0,1,0,1,3,0,2,15,11,0,3,46,76,34,0,5,161,430,475,111,0,8,601,2886,
%T 4640,2771,361,0,13,2208,19215,56541,48980,16451,1172,0,21,8053,
%U 127535,688999,1089035,514655,97160,3809,0,34,29415,847604,8334338,24209608,20993054
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .0.....1.......1.........2............3..............5................8
%C .0.....3......15........46..........161............601.............2208
%C .0....11......76.......430.........2886..........19215...........127535
%C .0....34.....475......4640........56541.........688999..........8334338
%C .0...111....2771.....48980......1089035.......24209608........535192095
%C .0...361...16451....514655.....20993054......849467774......34271733937
%C .0..1172...97160...5421003....404225195....29810775827....2195619257236
%C .0..3809..574671..57068484...7787623959..1046322460741..140685735128595
%C .0.12377.3397622.600825641.150008013842.36721875744312.9013655138528774
%H R. H. Hardin, <a href="/A302381/b302381.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F k=3: [order 11]
%F k=4: [order 26]
%F k=5: [order 84] for n>86
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
%F n=3: [order 14] for n>15
%F n=4: [order 42] for n>43
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..1
%e ..0..1..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..1. .1..0..0..0
%e ..0..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..1..0. .0..1..0..0
%e ..1..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..0..0. .0..0..1..1
%e ..1..1..0..0. .0..1..1..1. .0..0..1..1. .1..1..0..0. .1..1..0..0
%Y Column 2 is A180762.
%Y Row 1 is A000045(n-1).
%Y Row 2 is A232077(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Apr 06 2018