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%I #4 May 09 2018 10:06:48
%S 0,0,0,0,3,0,0,4,4,0,0,9,8,9,0,0,18,13,13,18,0,0,33,17,19,17,33,0,0,
%T 72,26,47,47,26,72,0,0,133,61,88,116,88,61,133,0,0,278,120,181,230,
%U 230,181,120,278,0,0,541,233,376,772,925,772,376,233,541,0,0,1084,515,878,1832
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0...0...0...0....0.....0......0......0.......0........0.........0.........0
%C .0...3...4...9...18....33.....72....133.....278......541......1084......2169
%C .0...4...8..13...17....26.....61....120.....233......515.......959......2203
%C .0...9..13..19...47....88....181....376.....878.....2001......4424.....10341
%C .0..18..17..47..116...230....772...1832....5500....15852.....43779....127396
%C .0..33..26..88..230...925...2516...8248...27317....89074....287896....945232
%C .0..72..61.181..772..2516..10024..35769..143364...546403...2127606...8299219
%C .0.133.120.376.1832..8248..35769.185874..883660..4100466..20201440..96805441
%C .0.278.233.878.5500.27317.143364.883660.4991758.27273238.158873103.901602511
%H R. H. Hardin, <a href="/A304263/b304263.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) +3*a(n-2) -4*a(n-3) -6*a(n-4) +4*a(n-5) for n>6
%F k=3: [order 17] for n>18
%F k=4: [order 63] for n>64
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..1..1. .0..0..0..1. .0..1..1..0. .0..1..1..0
%e ..1..0..1..1. .1..1..0..0. .1..1..0..0. .0..1..0..1. .0..1..1..0
%e ..1..1..1..0. .1..1..1..0. .1..0..1..0. .1..0..0..1. .0..1..1..0
%e ..0..0..1..1. .0..0..1..0. .0..0..1..1. .1..1..1..0. .0..1..1..0
%e ..1..0..0..0. .1..0..0..1. .1..1..0..0. .0..0..0..1. .0..1..1..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 09 2018
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