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%I #4 Mar 18 2018 08:32:39
%S 1,2,2,4,7,4,8,18,18,8,16,50,45,50,16,32,138,116,116,138,32,64,383,
%T 293,302,293,383,64,128,1063,735,726,726,735,1063,128,256,2951,1844,
%U 1709,1649,1709,1844,2951,256,512,8193,4626,3996,3649,3649,3996,4626,8193,512
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4.....8....16....32.....64....128....256....512....1024....2048
%C ...2....7....18....50...138...383...1063...2951...8193..22748...63161..175370
%C ...4...18....45...116...293...735...1844...4626..11611..29151...73200..183828
%C ...8...50...116...302...726..1709...3996...9346..21891..51367..120680..283746
%C ..16..138...293...726..1649..3649...8035..17751..39436..88008..197077..442264
%C ..32..383...735..1709..3649..7600..15802..33150..70311.150532..324443..702447
%C ..64.1063..1844..3996..8035.15802..31172..62375.126931.262036..546825.1149471
%C .128.2951..4626..9346.17751.33150..62375.119694.234839.469777..953721.1956225
%C .256.8193.11611.21891.39436.70311.126931.234839.446581.869959.1726691.3472128
%H R. H. Hardin, <a href="/A301323/b301323.txt">Table of n, a(n) for n = 1..612</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)
%F k=3: a(n) = 4*a(n-1) -3*a(n-2) -3*a(n-3) +2*a(n-4) +3*a(n-5) -2*a(n-6) for n>8
%F k=4: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-5) -3*a(n-7) +2*a(n-8) +a(n-9) -a(n-10) for n>13
%F k=5: [order 14] for n>16
%F k=6: [order 15] for n>19
%F k=7: [order 23] for n>28
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..0
%e ..0..1..0..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .1..0..1..1
%e ..1..0..1..0. .1..0..1..0. .0..1..0..0. .1..0..0..1. .1..0..0..1
%e ..0..1..0..1. .1..0..1..1. .0..1..1..0. .1..1..0..1. .1..1..0..1
%e ..1..0..1..0. .1..0..0..0. .0..0..1..0. .0..1..1..0. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A280598.
%Y Column 3 is A280599.
%Y Column 4 is A280600.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 18 2018
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