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%I #4 May 02 2018 07:56:05
%S 1,1,1,1,4,1,1,8,8,1,1,24,11,24,1,1,82,36,36,82,1,1,272,87,166,87,272,
%T 1,1,908,256,487,487,256,908,1,1,3076,684,2130,1150,2130,684,3076,1,1,
%U 10444,1932,7433,4964,4964,7433,1932,10444,1,1,35480,5308,30191,16431
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 4 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1....1......1......1.......1.......1........1.........1.........1
%C .1.....4....8.....24.....82.....272.....908.....3076.....10444.....35480
%C .1.....8...11.....36.....87.....256.....684.....1932......5308.....14809
%C .1....24...36....166....487....2130....7433....30191....112815....444834
%C .1....82...87....487...1150....4964...16431....68704....254498...1032541
%C .1...272..256...2130...4964...24985...88901...384168...1517262...6387363
%C .1...908..684...7433..16431...88901..308271..1437397...5832957..25738579
%C .1..3076.1932..30191..68704..384168.1437397..7577931..32153502.162027971
%C .1.10444.5308.112815.254498.1517262.5832957.32153502.148783767.818391800
%H R. H. Hardin, <a href="/A303888/b303888.txt">Table of n, a(n) for n = 1..263</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 16] for n>18
%F k=4: [order 38] for n>41
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..1..0
%e ..0..1..1..1. .0..1..1..0. .1..0..0..1. .1..0..0..1. .1..0..0..1
%e ..1..1..1..1. .0..1..1..1. .1..0..0..1. .1..0..0..1. .0..0..0..1
%e ..0..1..1..1. .1..1..1..0. .0..0..0..0. .1..0..0..1. .1..0..0..1
%e ..1..0..0..0. .0..0..1..0. .1..1..0..1. .0..1..1..0. .0..1..1..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 02 2018
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