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%I #4 Aug 09 2018 09:56:25
%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,4,6,6,4,0,0,9,4,26,4,9,0,0,22,5,88,
%T 88,5,22,0,0,53,10,301,220,301,10,53,0,0,130,36,1089,759,759,1089,36,
%U 130,0,0,320,34,4340,3303,4692,3303,4340,34,320,0,0,788,43,16696,11807,27620
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .0...0..0.....0.....0......0.......0.........0..........0...........0
%C .0...1..1.....2.....4......9......22........53........130.........320
%C .0...1..1.....6.....4......5......10........36.........34..........43
%C .0...2..6....26....88....301....1089......4340......16696.......64514
%C .0...4..4....88...220....759....3303.....11807......45995......161983
%C .0...9..5...301...759...4692...27620....167100.....990871.....5767582
%C .0..22.10..1089..3303..27620..163297...1242087....7872632....53760082
%C .0..53.36..4340.11807.167100.1242087..13125877..113996501..1068543427
%C .0.130.34.16696.45995.990871.7872632.113996501.1146051177.13578301848
%H R. H. Hardin, <a href="/A317871/b317871.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) -a(n-6)
%F k=3: [order 18]
%F k=4: [order 83] for n>86
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..0..1
%e ..1..0..0..0. .1..0..0..0. .1..0..1..0. .1..0..1..1. .1..0..0..1
%e ..1..1..0..1. .0..0..1..0. .0..1..1..1. .1..0..1..0. .0..0..1..0
%e ..0..0..0..1. .1..1..0..1. .1..0..1..0. .0..0..1..0. .1..0..0..1
%e ..1..0..1..0. .0..1..1..0. .0..1..0..1. .1..0..0..1. .1..0..1..0
%Y Column 2 is A317735.
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Aug 09 2018
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