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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having two distinct values, and new values 0..2 introduced in row major order
9

%I #5 Mar 31 2012 12:37:30

%S 7,34,34,164,280,164,792,2304,2304,792,3824,19008,32800,19008,3824,

%T 18464,156800,470736,470736,156800,18464,89152,1293568,6762544,

%U 11857440,6762544,1293568,89152,430464,10671616,97195728,299879808,299879808

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having two distinct values, and new values 0..2 introduced in row major order

%C Table starts

%C ......7.......34.........164...........792.............3824..............18464

%C .....34......280........2304.........19008...........156800............1293568

%C ....164.....2304.......32800........470736..........6762544...........97195728

%C ....792....19008......470736......11857440........299879808.........7597233712

%C ...3824...156800.....6762544.....299879808......13410113952.......602072007808

%C ..18464..1293568....97195728....7597233712.....602072007808.....48053885453696

%C ..89152.10671616..1397061008..192567994720...27070584920080...3846901518589376

%C .430464.88038400.20081495760.4881998439024.1217939572945968.308412624303464672

%H R. H. Hardin, <a href="/A209897/b209897.txt">Table of n, a(n) for n = 1..220</a>

%e Some solutions for n=4 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 14 2012