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%I #4 Mar 15 2018 18:51:58
%S 1,1,1,1,3,1,1,5,5,1,1,16,20,16,1,1,40,76,76,40,1,1,113,290,593,290,
%T 113,1,1,304,1245,4066,4066,1245,304,1,1,833,5160,30474,48588,30474,
%U 5160,833,1,1,2270,21819,224767,640673,640673,224767,21819,2270,1,1,6194,91713
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .1....1.....1........1..........1............1..............1................1
%C .1....3.....5.......16.........40..........113............304..............833
%C .1....5....20.......76........290.........1245...........5160............21819
%C .1...16....76......593.......4066........30474.........224767..........1677576
%C .1...40...290.....4066......48588.......640673........8265835........108469760
%C .1..113..1245....30474.....640673.....14914968......340365586.......7878577344
%C .1..304..5160...224767....8265835....340365586....13715723327.....560932609225
%C .1..833.21819..1677576..108469760...7878577344...560932609225...40555879417852
%C .1.2270.91713.12501697.1419225976.181974865532.22881004568048.2924437698122344
%H R. H. Hardin, <a href="/A300923/b300923.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -a(n-6)
%F k=3: [order 21] for n>22
%F k=4: [order 66] for n>68
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
%e ..0..1..1..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..1..0
%e ..1..1..1..1. .1..1..0..0. .0..1..0..1. .0..0..0..1. .0..0..0..1
%e ..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1
%e ..0..1..0..0. .0..1..1..0. .1..1..0..0. .0..1..0..1. .0..0..1..0
%Y Column 2 is A300533.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 15 2018
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