%I #4 Jul 24 2018 10:40:15

%S 1,2,2,4,4,4,8,12,12,8,16,24,28,24,16,32,64,60,60,64,32,64,184,211,

%T 168,211,184,64,128,432,597,674,674,597,432,128,256,1088,1619,2432,

%U 4798,2432,1619,1088,256,512,2944,4792,8255,24487,24487,8255,4792,2944,512,1024

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2.....4......8......16.......32........64.........128..........256

%C ...2....4....12.....24......64......184.......432........1088.........2944

%C ...4...12....28.....60.....211......597......1619........4792........13802

%C ...8...24....60....168.....674.....2432......8255.......29245.......105103

%C ..16...64...211....674....4798....24487....112675......602717......3142280

%C ..32..184...597...2432...24487...157007....995887.....7221707.....50355283

%C ..64..432..1619...8255..112675...995887...8436662....83084854....788831052

%C .128.1088..4792..29245..602717..7221707..83084854..1148371444..15185768273

%C .256.2944.13802.105103.3142280.50355283.788831052.15185768273.277147933683

%H R. H. Hardin, <a href="/A317238/b317238.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 13] for n>14

%F k=4: [order 65] for n>67

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A303794.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 24 2018