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%I #4 Mar 08 2018 12:26:36
%S 1,1,1,1,3,1,1,5,5,1,1,16,12,16,1,1,40,36,36,40,1,1,113,122,300,122,
%T 113,1,1,304,429,1436,1436,429,304,1,1,833,1585,8974,12951,8974,1585,
%U 833,1,1,2270,5755,52012,124543,124543,52012,5755,2270,1,1,6194,21084,311037
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 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....12......36.......122........429.........1585...........5755
%C .1...16....36.....300......1436.......8974........52012.........311037
%C .1...40...122....1436.....12951.....124543......1220365.......11917710
%C .1..113...429....8974....124543....1972991.....31434011......501719570
%C .1..304..1585...52012...1220365...31434011....831752031....21825406629
%C .1..833..5755..311037..11917710..501719570..21825406629...946782030618
%C .1.2270.21084.1845926.117661891.8058860856.577067248097.41212879288810
%H R. H. Hardin, <a href="/A300539/b300539.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 22] for n>24
%F k=4: [order 75] for n>78
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..1..1..0
%e ..1..1..0..0. .1..1..0..1. .0..1..1..0. .1..1..1..1. .1..0..1..1
%e ..1..1..1..1. .0..1..1..1. .0..1..0..0. .0..0..1..1. .1..1..1..1
%e ..0..1..0..1. .1..1..0..1. .0..0..1..0. .0..0..1..0. .0..0..0..1
%e ..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..0..0..0. .0..0..1..1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 08 2018