%I #4 Jan 19 2018 08:38:29
%S 0,1,1,0,4,0,1,4,4,1,0,16,0,16,0,1,48,11,11,48,1,0,88,26,161,26,88,0,
%T 1,240,46,478,478,46,240,1,0,704,204,2459,5938,2459,204,704,0,1,1600,
%U 696,15248,22133,22133,15248,696,1600,1,0,4032,1493,78163,206239,255029
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0....1....0......1........0.........1...........0.............1
%C .1....4....4.....16.......48........88.........240...........704
%C .0....4....0.....11.......26........46.........204...........696
%C .1...16...11....161......478......2459.......15248.........78163
%C .0...48...26....478.....5938.....22133......206239.......2539477
%C .1...88...46...2459....22133....255029.....4095727......62979342
%C .0..240..204..15248...206239...4095727...112275165....2871621220
%C .1..704..696..78163..2539477..62979342..2871621220..141892377970
%C .0.1600.1493.390424.16116493.804773211.62756244756.4903035588074
%H R. H. Hardin, <a href="/A298454/b298454.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-2)
%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)
%F k=3: [order 17] for n>18
%F k=4: [order 53] for n>56
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..0..1..1. .0..0..0..0. .0..1..1..0. .0..0..1..1
%e ..1..0..1..1. .1..1..1..1. .1..1..0..0. .0..1..1..0. .0..0..1..1
%e ..0..0..0..1. .1..1..0..0. .1..1..1..1. .0..0..1..1. .1..1..1..1
%e ..0..0..1..1. .1..1..0..0. .0..1..0..0. .0..0..0..1. .0..0..1..1
%e ..1..1..1..1. .1..1..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 19 2018