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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having two distinct values, and new values 0..3 introduced in row major order
9

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

%S 7,34,34,173,302,173,930,2721,2721,930,5193,25505,43209,25505,5193,

%T 29782,244208,712829,712829,244208,29782,173789,2377378,11912459,

%U 20873080,11912459,2377378,173789,1025274,23398105,201392025,617966001,617966001

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having two distinct values, and new values 0..3 introduced in row major order

%C Table starts

%C .......7........34.........173............930.............5193

%C ......34.......302........2721..........25505...........244208

%C .....173......2721.......43209.........712829.........11912459

%C .....930.....25505......712829.......20873080........617966001

%C ....5193....244208....11912459......617966001......32449786403

%C ...29782...2377378...201392025....18479672376....1723218327331

%C ..173789..23398105..3428713825...555404234236...91909548662623

%C .1025274.231987361.58668627061.16753667272666.4917823780419687

%H R. H. Hardin, <a href="/A209814/b209814.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions for n=4 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 13 2012