%I #4 Jan 23 2018 12:28:32

%S 0,0,0,0,1,0,0,3,3,0,0,6,8,6,0,0,17,26,26,17,0,0,41,138,125,138,41,0,

%T 0,104,611,1218,1218,611,104,0,0,261,2880,8617,20959,8617,2880,261,0,

%U 0,655,13727,71334,285085,285085,71334,13727,655,0,0,1646,65070,577595,4228781

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0...0.....0.......0.........0............0..............0................0

%C .0...1.....3.......6........17...........41............104..............261

%C .0...3.....8......26.......138..........611...........2880............13727

%C .0...6....26.....125......1218.........8617..........71334...........577595

%C .0..17...138....1218.....20959.......285085........4228781.........62707643

%C .0..41...611....8617....285085......7087666......193309200.......5247911837

%C .0.104..2880...71334...4228781....193309200.....9557110072.....471778534219

%C .0.261.13727..577595..62707643...5247911837...471778534219...42384213387355

%C .0.655.65070.4700651.929296248.142315671147.23254989974319.3802910270886730

%H R. H. Hardin, <a href="/A298629/b298629.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)

%F k=3: [order 11] for n>12

%F k=4: [order 48]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297972.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 23 2018