%I #4 May 23 2018 16:04:39

%S 0,1,1,1,3,1,2,11,11,2,3,10,14,10,3,5,51,31,31,51,5,8,165,99,42,99,

%T 165,8,13,306,206,255,255,206,306,13,21,993,455,862,2715,862,455,993,

%U 21,34,2867,1321,2200,9499,9499,2200,1321,2867,34,55,6818,3108,8807,30457

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0....1....1.....2.......3.......5........8........13.........21..........34

%C ..1....3...11....10......51.....165......306.......993.......2867........6818

%C ..1...11...14....31......99.....206......455......1321.......3108........7353

%C ..2...10...31....42.....255.....862.....2200......8807......33055......106158

%C ..3...51...99...255....2715....9499....30457....225009....1046863.....4428355

%C ..5..165..206...862....9499...28477...119835....975646....4538929....21859448

%C ..8..306..455..2200...30457..119835...640900...6449924...41160483...271320922

%C .13..993.1321..8807..225009..975646..6449924.108290760..866160130..7324403720

%C .21.2867.3108.33055.1046863.4538929.41160483.866160130.7783586346.84091029541

%H R. H. Hardin, <a href="/A305015/b305015.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

%F k=3: [order 17] for n>18

%F k=4: [order 69] for n>70

%e Some solutions for n=5 k=4

%e ..0..1..0..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..0..1

%e ..0..0..0..1. .0..1..1..0. .0..0..0..0. .0..0..0..1. .0..1..0..1

%e ..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..1..0. .1..1..1..1

%e ..1..0..1..0. .0..1..1..0. .1..1..0..1. .0..1..1..1. .0..1..0..1

%e ..0..0..0..1. .1..0..1..1. .0..0..0..0. .0..0..0..1. .0..1..0..1

%Y Column 1 is A000045(n-1).

%Y Column 2 is A304052.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 23 2018