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%I #4 Apr 24 2018 10:43:32
%S 1,2,2,4,8,4,8,29,32,8,16,105,170,128,16,32,384,948,1033,512,32,64,
%T 1405,5237,9110,6369,2048,64,128,5135,29009,79377,89371,39098,8192,
%U 128,256,18766,160590,692636,1243692,872026,240109,32768,256,512,68589,888993
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1......2.......4.........8..........16............32..............64
%C ...2......8......29.......105.........384..........1405............5135
%C ...4.....32.....170.......948........5237.........29009..........160590
%C ...8....128....1033......9110.......79377........692636.........6051850
%C ..16....512....6369.....89371.....1243692......17247543.......239939422
%C ..32...2048...39098....872026....19374638.....427097893......9459086839
%C ..64...8192..240109...8511918...302023677...10589284528....373571747330
%C .128..32768.1476141..83188773..4716032889..263136262937..14793218857797
%C .256.131072.9071642.812770434.73624207904.6538180319944.585806882371397
%H R. H. Hardin, <a href="/A303469/b303469.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1)
%F k=3: a(n) = 7*a(n-1) -5*a(n-2) +20*a(n-3) -144*a(n-4) +72*a(n-5) for n>6
%F k=4: [order 20] for n>21
%F k=5: [order 93] for n>94
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F n=3: [order 14] for n>15
%F n=4: [order 49] for n>50
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
%e ..1..1..1..1. .1..0..1..1. .1..1..1..0. .1..0..1..0. .1..0..0..0
%e ..0..0..0..0. .0..1..0..0. .1..1..1..1. .0..0..1..1. .0..1..1..0
%e ..0..1..1..0. .0..1..0..1. .0..0..1..0. .0..0..0..0. .0..1..1..0
%e ..1..0..0..0. .0..0..1..0. .0..0..1..0. .1..1..1..1. .1..1..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A004171(n-1).
%Y Row 1 is A000079(n-1).
%Y Row 2 is A302266.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 24 2018
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