%I #7 Dec 11 2015 21:30:46

%S 81,60,60,162,246,162,486,1122,1122,486,1458,5118,7812,5118,1458,4374,

%T 23346,54450,54450,23346,4374,13122,106494,379602,580986,379602,

%U 106494,13122,39366,485778,2646540,6204438,6204438,2646540,485778,39366,118098

%N T(n,k) = number of (n+1) X (k+1) 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.

%C Table starts

%C ....81......60.......162........486.........1458...........4374

%C ....60.....246......1122.......5118........23346.........106494

%C ...162....1122......7812......54450.......379602........2646540

%C ...486....5118.....54450.....580986......6204438.......66274542

%C ..1458...23346....379602....6204438....101596896.....1664748270

%C ..4374..106494...2646540...66274542...1664748270....41869995708

%C .13122..485778..18451530..707982258..27284864220..1053631126386

%C .39366.2215902.128643282.7563227466.447232269654.26519876081106

%H R. H. Hardin, <a href="/A206150/b206150.txt">Table of n, a(n) for n = 1..364</a>

%e Some solutions for n=4, k=3:

%e ..2..1..2..1....0..1..2..1....0..2..0..1....2..0..2..0....0..1..2..0

%e ..1..2..0..2....1..0..1..2....1..0..2..0....0..1..0..1....1..0..1..2

%e ..2..0..1..0....2..1..2..0....2..1..0..1....1..2..1..2....0..2..0..1

%e ..1..2..0..1....0..2..0..1....0..2..1..2....0..1..0..1....1..0..1..0

%e ..2..0..2..0....2..0..1..2....1..0..2..0....2..0..1..0....2..1..2..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 04 2012