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

%I #5 Mar 31 2012 12:37:34

%S 7,59,59,549,1316,549,5167,29647,29647,5167,48689,668468,1596154,

%T 668468,48689,458859,15072359,85979301,85979301,15072359,458859,

%U 4324477,339846892,4631193134,11066406572,4631193134,339846892,4324477,40755719

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

%C Table starts

%C ........7...........59.............549................5167

%C .......59.........1316...........29647..............668468

%C ......549........29647.........1596154............85979301

%C .....5167.......668468........85979301.........11066406572

%C ....48689.....15072359......4631193134.......1424263182001

%C ...458859....339846892....249456180709.....183306323524536

%C ..4324477...7662761615..13436785945910...23591974220786341

%C .40755719.172777559876.723763304576749.3036345393226822100

%H R. H. Hardin, <a href="/A210404/b210404.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions for n=4 k=3

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

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..3..1

%e ..1..2..1..3....0..0..0..0....0..0..0..0....0..0..0..0....1..2..2..2

%e ..1..3..3..2....0..0..0..0....0..0..0..0....0..0..0..0....1..3..0..1

%e ..1..0..1..1....1..2..1..2....1..2..3..1....0..0..0..0....1..0..1..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 21 2012